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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+51x^78+126x^79+181x^80+262x^81+244x^82+350x^83+392x^84+470x^85+547x^86+610x^87+727x^88+632x^89+664x^90+560x^91+489x^92+402x^93+312x^94+268x^95+210x^96+192x^97+123x^98+92x^99+67x^100+72x^101+38x^102+36x^103+36x^104+18x^105+5x^106+6x^107+8x^108+1x^128

The gray image is a linear code over GF(2) with n=356, k=13 and d=156.
This code was found by Heurico 1.16 in 8.37 seconds.