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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+174x^87+77x^88+120x^89+380x^90+572x^91+362x^92+116x^93+64x^94+162x^95+8x^96+4x^97+2x^98+4x^99+1x^102+1x^174

The gray image is a linear code over GF(2) with n=728, k=11 and d=348.
This code was found by Heurico 1.16 in 62.3 seconds.