The generator matrix

 1  0  1  1  1 X^3+X^2+X  X  1  1 X^3+X^2  1  1  1  1  1 X^3+X^2+X  1 X^3  1 X^2+X  1  1  1  1  1  1 X^3+X  1 X^2  1  1  1 X^3+X X^3+X^2 X^3+X^2  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1  1 X^3 X^2+1  1 X^2+X+1 X^3+X^2+X X^3+1 X^3+X X+1  1 X^3+X^2  1 X^2+X+1  1 X^2  1  X X^2+1 X^2 X^3+X^2+1  1 X+1  1 X^2+X X^3+X X^2+X  1  1  1 X+1  0
 0  0 X^2  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^3  0 X^3 X^2  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^2  0  0 X^3+X^2  0 X^3 X^3 X^3 X^3  0  0  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0  0  0 X^3 X^3  0  0  0  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  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+21x^32+178x^33+260x^34+600x^35+557x^36+892x^37+550x^38+592x^39+247x^40+158x^41+18x^42+4x^43+3x^44+4x^45+2x^46+4x^47+3x^48+2x^50

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 0.141 seconds.