The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X^2+X  1 X^3+X^2  1  1 X^3+X  1  1  1  1 X^2  X  1  1  1  1 X^3  1 X^3+X^2+X  1  1  1 X^2  1  X  1  1 X^3+X^2  1 X^3+X  1  1  1 X^2+X  0  1  1  1  0 X^2+X X^3+X^2 X^3+X  0 X^2+X  0 X^2+X X^3+X^2 X^2+X X^3+X  0 X^3+X^2 X^3+X X^3+X^2 X^3+X  1  1  1  1  1 X^3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1
 0  1 X+1 X^3+X^2+X X^3+X^2+1  1  X X+1  1 X^3+X^2 X^2+1  1 X^2+X+1  1 X^3  1  1 X^2+X X^3+X^2+X+1 X^3+1 X^3+X  1  1  X X^2 X^3+X+1 X^3+X^2+1  1 X^2  1 X^3+X^2+X X^2+X+1  1  1 X^3  1 X^3+X^2+X X^3+X^2+1  1 X+1  1 X^3+X^2  X  1  1  1  0 X^3+X^2+X+1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2 X^2+X X^3+X^2 X^2+X X^3 X^3+X X^3+X^2 X^3+X^2+X  0 X^3+X^2  X  0  X  0 X^3+X^2+X X^3+X^2+X+1 X^2+1 X^3+X+1 X^3+1 X^3+X^2 X^3+X+1 X^2+1 X^3+1 X^3+X+1  0
 0  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2  0  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^2 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2  0  0 X^3 X^3  0 X^2  0 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3  0 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3  0 X^3+X^2  0  0 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3  0  0
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0  0  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+86x^87+291x^88+224x^89+534x^90+236x^91+170x^92+120x^93+88x^94+46x^95+185x^96+40x^97+8x^98+16x^99+1x^112+1x^114+1x^130

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 0.953 seconds.