The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X X 2 X X X X X 0 X 0 X X X X 0 1 X 1 1 1 1 2 1 X 1 X 1 0 1 2 1 1 1 X 0 X 1
0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 2 X X+2 2 X X X 2 X 0 X 2 X+2 X X+2 X+2 X+2 X+2 X 2 X+2 0 X+2 2 X X+2 X 0 X+2 2 X X+2 X X 2 X+2 2 X 2 2 X X 0 X X+2 X+2 X 2 2 2 X+2 X X 0 X 2 0 X+2 0 0 0 2 X X X X+2 X 2 0
0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X X 0 X+2 2 0 X+2 X X X+2 X+2 2 0 X+2 0 2 X+2 X 0 2 2 2 X 0 X X+2 X+2 X X 2 X 2 X 2 0 0 0 2 X X+2 2 X X X X+2 2 X 2 0 2 X 0 0 0 X 0 2 2 X 2 X X 2 X 2 0 2 0 0 0
0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 2 X+2 X+2 X 0 2 0 2 X X X 2 X 0 X+2 0 X X+2 0 2 2 X X X+2 0 2 X 0 2 X+2 X+2 0 2 2 X 2 2 X+2 2 0 X X X 2 2 0 0 X+2 0 0 X+2 0 X+2 0 X X+2 X+2 0 X X+2 X+2 X X+2 X+2 2 X+2 0 X 2
0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 X+2 2 X+2 X X+2 2 2 X 0 X+2 2 X+2 X+2 X X+2 X 0 X+2 X+2 0 X 0 2 2 0 X+2 2 2 2 0 X X X+2 X+2 0 X+2 X+2 X+2 X+2 X 0 X 2 2 X+2 X+2 X X X+2 X+2 X 0 0 0 X X+2 X X X+2 X X X+2 2 0 X+2 X 2 X 2
0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X X+2 0 2 2 0 X 0 X 2 2 X+2 X+2 X+2 X+2 0 2 2 2 2 X+2 0 0 X+2 X+2 X+2 X X X+2 X+2 2 2 2 0 0 X X+2 0 X 0 0 0 X+2 2 X+2 0 2 X 0 0 X+2 0 X 0 X+2 X+2 X+2 X+2 2 0 2 2 X X+2 0 X+2 2 X+2 0
0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 0 2 2 2 2 0 2 0 0 0 0 0 0 2 2 2 2 2 2 0 2 2 0 0 2 0 2 2 2 2 0 2 0 2 0 2 2 0 2 2 2 0
generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.
Homogenous weight enumerator: w(x)=1x^0+61x^74+92x^75+159x^76+266x^77+315x^78+400x^79+511x^80+594x^81+797x^82+888x^83+1000x^84+1228x^85+1301x^86+1358x^87+1325x^88+1200x^89+1012x^90+856x^91+673x^92+574x^93+447x^94+364x^95+256x^96+182x^97+189x^98+112x^99+86x^100+44x^101+33x^102+22x^103+19x^104+8x^105+4x^106+4x^107+2x^108+1x^122
The gray image is a code over GF(2) with n=348, k=14 and d=148.
This code was found by Heurico 1.16 in 31.2 seconds.