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  1  1  1  1  1  1  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^3 X^2 X^2 X^3 X^2 X^3 X^2 X^2  0 X^3+X^2 X^3  0 X^3+X^2 X^3 X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^3+X^2  0 X^2  0 X^3 X^2 X^2 X^2 X^3  0 X^3+X^2 X^3  0 X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3+X^2  0 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^3 X^2  0 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3  0 X^2 X^3 X^3+X^2 X^2 X^3  0 X^2 X^3 X^3 X^2 X^2 X^3 X^3 X^2 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^3 X^3 X^2 X^2  0 X^3+X^2 X^3  0 X^2 X^3 X^3  0 X^3+X^2 X^2  0 X^3 X^2
 0  0  0 X^3  0  0 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0  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  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0  0 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0  0  0  0 X^3  0  0 X^3
 0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  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  0 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+59x^86+96x^87+68x^88+1600x^91+68x^94+96x^95+59x^96+1x^182

The gray image is a linear code over GF(2) with n=728, k=11 and d=344.
This code was found by Heurico 1.16 in 3.44 seconds.