The generator matrix

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

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+202x^86+305x^88+1042x^90+298x^92+190x^94+2x^96+6x^98+1x^100+1x^172

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 2.03 seconds.