The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1  1  X X^2  1  X  1  1  X  1  1  X  1  1  X X^2  X  1  1  X  0  1  1  1  1  1  0 X^2  1 X^2+X  1  1 X^2+X  1  1 X^2  1 X^2 X^2+X  X  1  1  0 X^2+X  X X^2+X X^2  1  1  1  1  1  0  1  0  1 X^2+X  X X^2 X^2  1  0 X^2+X  1  1  X  1 X^2  1  1  1  X  0  1  1  1
 0  1  0  0  0  0 X+1  X X^2 X+1  1 X^2  1  1  1  X X^2+X  1  1 X^2+X  0  X X^2  0 X^2+X+1  1  1  1 X+1  1  1 X^2  X X^2  1  X X^2  1  1 X+1  1  1 X^2+X+1 X^2  X  1  X X^2+1  1  1  1 X^2 X^2+X X^2+X  1  X  0  1 X^2+X X^2+X+1  X X^2 X^2+X  1  X  1  0  1 X^2+X  1 X^2  X  0 X^2+X  X X+1  1 X^2+X+1 X^2+X  X  X X^2+X  1 X^2  1 X^2  0
 0  0  1  0  0  0  1 X+1  1 X^2+1 X^2 X^2+1  1 X^2+1  1 X^2+X+1  1  1  X  1 X^2+X+1 X^2 X^2  X X^2 X^2+X X+1 X^2+X  0 X^2+X X^2+X+1  0  X X+1 X^2 X^2+X X^2+1  1 X^2+X+1 X+1 X^2+X X^2+1 X^2+X  1 X^2+X  X  X  1 X^2  X X^2+X+1 X^2+X+1  0  1 X^2 X^2  1 X^2+1 X+1 X^2+1  X X^2  0  0 X^2 X+1  1  0 X^2 X^2  1  X  1 X^2+X  X  X X^2 X^2+X  1 X^2+X+1 X^2+X+1 X^2  0  X X^2+X  1  0
 0  0  0  1  0  1 X^2 X^2+1  1 X+1 X^2+1 X^2+X  X X^2+X X+1 X^2+X+1 X^2 X^2+1  0 X+1  0  X  1 X+1 X^2+X+1 X^2+X X+1 X^2+X+1  1  X  0  1 X^2+X X^2+X+1  0 X^2+X+1 X^2+X  1  X  0 X^2 X^2+X X+1 X+1  X X+1  0 X+1 X^2+X+1 X^2 X^2+1 X^2+X+1 X^2+1  1  0  1  X  X X^2 X+1  0  X X+1  1  X X^2+1  0 X^2+X+1  1  0 X^2+1  1 X+1  1 X+1  X  1 X^2+X+1 X^2+X  X X^2+X X^2+X X^2+1  1  1 X^2  0
 0  0  0  0  1  1 X^2+1  X X+1 X^2+1 X^2+X X^2+1  0  1  0 X^2+X+1 X^2+X+1 X^2 X+1 X^2 X^2+X X^2+1 X+1  0 X^2  1 X^2+1 X+1  1  X X^2+X  0 X^2+1 X^2+X+1 X^2+1  X X^2+X X^2+X+1 X^2+X X^2+X X^2 X^2+1  1  1  0  0  1  X X+1 X^2+1  0 X^2+X X+1  0 X+1 X^2+X+1  0 X^2+1 X+1 X^2+1 X^2  0  1 X+1 X+1 X^2+X+1  1 X+1 X+1 X^2+X+1 X+1 X+1  X X+1 X^2  1  0 X+1 X^2  X  X  1  X X^2+1 X^2+X+1 X^2+1  0
 0  0  0  0  0  X  0  X  X X^2+X  X X^2 X^2 X^2 X^2+X X^2+X  0  X  0 X^2+X  0 X^2  X X^2+X  X  0  X  X X^2+X  0 X^2 X^2+X  0  X X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X  X  0  0  X X^2 X^2+X X^2  0 X^2+X X^2  0 X^2 X^2 X^2  0 X^2+X X^2+X  X X^2  X  0 X^2+X X^2+X  0  0  0  0 X^2+X X^2+X  0 X^2 X^2 X^2+X X^2+X X^2+X X^2 X^2+X  X  0  X X^2+X  0 X^2+X X^2 X^2+X  0

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+66x^74+380x^75+786x^76+1486x^77+2124x^78+2858x^79+3707x^80+5416x^81+6157x^82+7730x^83+8610x^84+10284x^85+10140x^86+11196x^87+10324x^88+10308x^89+8848x^90+8084x^91+6314x^92+5246x^93+3720x^94+2842x^95+1766x^96+1240x^97+621x^98+330x^99+210x^100+120x^101+64x^102+48x^103+26x^104+12x^105+4x^106+4x^107

The gray image is a linear code over GF(2) with n=348, k=17 and d=148.
This code was found by Heurico 1.13 in 287 seconds.