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

generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+69x^80+80x^84+96x^86+1536x^87+143x^88+32x^90+60x^92+26x^96+4x^100+1x^168

The gray image is a linear code over GF(2) with n=696, k=11 and d=320.
This code was found by Heurico 1.16 in 0.672 seconds.