The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+120x^89+245x^90+338x^91+221x^92+64x^93+9x^94+10x^95+1x^96+12x^97+1x^112+1x^114+1x^130

The gray image is a linear code over GF(2) with n=728, k=10 and d=356.
This code was found by Heurico 1.16 in 4.33 seconds.