The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+236x^76+604x^77+1027x^78+1780x^79+2080x^80+2924x^81+3119x^82+4058x^83+4051x^84+5066x^85+4794x^86+5796x^87+4830x^88+5534x^89+4340x^90+4090x^91+3086x^92+2802x^93+1897x^94+1278x^95+851x^96+590x^97+289x^98+188x^99+91x^100+72x^101+18x^102+26x^103+6x^104+8x^105+4x^106

The gray image is a linear code over GF(2) with n=348, k=16 and d=152.
This code was found by Heurico 1.13 in 73.1 seconds.