The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+354x^88+360x^89+354x^90+180x^91+257x^92+216x^93+146x^94+52x^95+60x^96+24x^97+24x^98+8x^100+6x^104+4x^106+1x^124+1x^128

The gray image is a linear code over GF(2) with n=728, k=11 and d=352.
This code was found by Heurico 1.16 in 2.95 seconds.