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  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  1  1  1  1  X  X  1  1
 0 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3
 0  0 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3
 0  0  0 X^3  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3
 0  0  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3
 0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+70x^72+81x^76+96x^78+1536x^79+149x^80+32x^82+42x^84+35x^88+5x^92+1x^152

The gray image is a linear code over GF(2) with n=632, k=11 and d=288.
This code was found by Heurico 1.16 in 0.516 seconds.