The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  X  1
 0 X^3  0  0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0
 0  0 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0
 0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0
 0  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0
 0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 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+41x^32+21x^34+32x^35+144x^36+576x^37+144x^38+32x^39+16x^42+6x^48+10x^50+1x^66

The gray image is a linear code over GF(2) with n=296, k=10 and d=128.
This code was found by Heurico 1.16 in 0.031 seconds.