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  X  1  0  1  X  X  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X X^3+X^2 X^3 X^3+X^2+X X^2 X^3+X  0 X^2+X X^3+X X^3+X^2 X^2+X  0 X^3+X X^3+X^2  0 X^2+X X^3+X X^3+X^2 X^3 X^2+X X^3+X X^2 X^3+X^2+X  0  X X^3+X^2 X^3 X^2 X^3+X^2+X  X X^2+X  0 X^3 X^3+X^2+X X^3+X^2 X^3+X X^2  X  0 X^3+X  X  0 X^3  X X^3 X^3+X X^3+X^2 X^3+X^2 X^2 X^2+X X^2+X X^3+X^2+X X^2 X^3+X^2+X  0 X^2+X  0 X^3 X^3 X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2 X^3+X^2 X^2 X^2+X X^3+X^2+X X^2 X^3+X X^3+X  X X^3+X^2+X X^3+X^2+X X^2+X  X  X X^2+X X^2+X X^2+X X^2+X  0
 0  0 X^3  0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 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 X^3  0 X^3 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  0  0  0  0  0 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 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 X^3 X^3 X^3  0  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 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+60x^86+120x^87+102x^88+96x^89+286x^90+720x^91+289x^92+96x^93+96x^94+120x^95+53x^96+6x^98+2x^100+1x^172

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 1 seconds.