The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+79x^32+84x^33+261x^34+608x^35+566x^36+920x^37+556x^38+608x^39+241x^40+84x^41+77x^42+6x^44+2x^48+1x^50+1x^56+1x^58

The gray image is a linear code over GF(2) with n=296, k=12 and d=128.
This code was found by Heurico 1.16 in 0.125 seconds.