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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+68x^85+224x^86+234x^87+351x^88+464x^89+306x^90+964x^91+319x^92+420x^93+196x^94+182x^95+179x^96+52x^97+58x^98+44x^99+13x^100+4x^101+16x^102+1x^160

The gray image is a linear code over GF(2) with n=728, k=12 and d=340.
This code was found by Heurico 1.16 in 1.28 seconds.