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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+221x^84+56x^85+272x^86+216x^87+478x^88+496x^89+720x^90+496x^91+411x^92+216x^93+244x^94+56x^95+107x^96+68x^98+28x^100+4x^102+1x^104+4x^106+1x^160

The gray image is a linear code over GF(2) with n=720, k=12 and d=336.
This code was found by Heurico 1.16 in 11.8 seconds.