The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+274x^77+601x^78+1292x^79+1683x^80+1966x^81+2654x^82+3202x^83+4003x^84+4464x^85+4777x^86+5082x^87+5412x^88+5302x^89+4988x^90+4486x^91+3848x^92+3312x^93+2609x^94+2008x^95+1329x^96+986x^97+606x^98+296x^99+178x^100+68x^101+49x^102+16x^103+23x^104+10x^105+4x^106+2x^108+2x^109+2x^111+1x^124

The gray image is a linear code over GF(2) with n=352, k=16 and d=154.
This code was found by Heurico 1.13 in 73.9 seconds.