The generator matrix

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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+57x^86+346x^87+288x^88+282x^89+262x^90+244x^91+191x^92+184x^93+63x^94+88x^95+31x^96+6x^97+1x^98+2x^111+1x^116+1x^130

The gray image is a linear code over GF(2) with n=720, k=11 and d=344.
This code was found by Heurico 1.16 in 0.907 seconds.