The generator matrix

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

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+14x^88+160x^89+94x^90+480x^91+144x^92+96x^93+32x^95+1x^112+1x^114+1x^130

The gray image is a linear code over GF(2) with n=728, k=10 and d=352.
This code was found by Heurico 1.16 in 0.562 seconds.