The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+141x^80+292x^81+454x^82+584x^83+621x^84+616x^85+673x^86+688x^87+623x^88+588x^89+551x^90+516x^91+441x^92+408x^93+259x^94+256x^95+173x^96+72x^97+73x^98+60x^99+26x^100+8x^101+32x^102+8x^103+18x^104+6x^106+4x^108

The gray image is a linear code over GF(2) with n=352, k=13 and d=160.
This code was found by Heurico 1.16 in 4.91 seconds.