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  X X^2  X  X X^2  1  X  1  X  0  1  0  1  1  1  X X^2  X  1 X^2  1  1 X^2  X  0  1  X X^2  1  X  1  X  1  1  1  1 X^2  X  1  1  1  1  1  X  1  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2+X X^2+X  X X^2  X  0  X X^2  0 X^2+X  X X^2 X^2  X X^2 X^2  X  X X^2 X^2+X X^2+X  X  X  X  0 X^2  0  0  X X^2  0  X  X X^2+X X^2  0  0 X^2+X  0 X^2 X^2+X X^2+X X^2  X  X X^2  X X^2 X^2+X X^2  X  X  X X^2+X  X X^2 X^2+X  0  0  X  0 X^2 X^2  X  X  0  0  X  X X^2 X^2 X^2 X^2 X^2+X
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2 X^2 X^2  X X^2  X X^2  X X^2+X X^2+X  0  X  0  X  X  0 X^2  X X^2 X^2+X X^2 X^2 X^2+X X^2  X  X X^2  0  X X^2  X X^2+X X^2+X X^2  X  X  0 X^2+X X^2 X^2+X  X  X X^2+X X^2  X  X X^2  X X^2+X X^2+X X^2+X X^2  0  X X^2 X^2  0 X^2+X X^2  X  0 X^2+X  0 X^2+X X^2+X X^2+X  X X^2 X^2+X X^2 X^2+X  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  0 X^2+X X^2+X X^2+X  X X^2+X  0 X^2 X^2  X  0  0  X  0  0  X  X  0 X^2 X^2+X  0  X  0  X X^2  X X^2+X X^2  X  X X^2 X^2 X^2  0 X^2 X^2+X X^2+X  0  X X^2+X  X  X  X  0  0  X X^2 X^2+X  X  X X^2+X  X X^2+X  0 X^2+X X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2  X  0 X^2 X^2 X^2+X X^2+X X^2  X X^2+X X^2+X  X  X
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X  X X^2 X^2  0 X^2+X  X X^2  0 X^2  X  0  X  X  X X^2+X X^2  0 X^2+X X^2  0  0 X^2+X  X X^2+X X^2 X^2+X  X  X X^2 X^2 X^2+X  X X^2+X X^2+X X^2+X  X X^2+X X^2 X^2  0 X^2 X^2+X X^2  X  X X^2 X^2  0 X^2+X  X X^2 X^2  0  0 X^2+X X^2 X^2+X X^2+X X^2+X  0 X^2+X X^2+X X^2+X  0  X X^2+X  0 X^2+X X^2 X^2+X  0 X^2  0  X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 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+54x^77+128x^78+174x^79+232x^80+290x^81+311x^82+402x^83+463x^84+528x^85+643x^86+668x^87+693x^88+650x^89+563x^90+510x^91+430x^92+340x^93+271x^94+190x^95+141x^96+128x^97+98x^98+72x^99+76x^100+54x^101+26x^102+22x^103+8x^104+4x^105+8x^106+8x^107+3x^108+2x^111+1x^128

The gray image is a linear code over GF(2) with n=352, k=13 and d=154.
This code was found by Heurico 1.16 in 8.81 seconds.