The generator matrix

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

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+119x^32+148x^33+380x^34+516x^35+451x^36+984x^37+400x^38+504x^39+286x^40+148x^41+92x^42+4x^43+36x^44+24x^46+2x^48+1x^52

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 0.312 seconds.