The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  X X^3  1  1 X^3 X^3 X^3  1  1  1  X X^2  1  X  1
 0  X  0  X  0 X^3 X^2+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X X^2+X X^3+X X^3+X^2+X X^3 X^3 X^3 X^2 X^3+X^2+X  X X^3 X^3+X^2+X  X  X X^3+X^2 X^2 X^2+X X^2+X X^2 X^2  0 X^2+X X^3
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^3+X^2 X^3  0 X^3+X^2  X X^2+X X^3+X X^2+X X^2+X  X X^2 X^3+X^2+X  X  0 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X X^3+X  X  X X^2+X X^2 X^3 X^3+X^2+X  X X^2+X X^2+X X^2
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3
 0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  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+67x^32+186x^33+309x^34+552x^35+526x^36+910x^37+534x^38+472x^39+272x^40+110x^41+63x^42+64x^43+14x^44+10x^45+5x^46+1x^54

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 0.188 seconds.