The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  X  X X^2  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X  0 X^3+X X^3 X^3+X X^3+X^2 X^2+X X^2 X^3+X^2+X  0 X^3+X X^3+X^2 X^2 X^2+X X^3+X^2+X  0 X^3 X^3 X^2+X X^3+X  X X^3+X^2 X^2+X X^3+X^2+X X^2+X X^3 X^3+X^2  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0  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 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 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+27x^32+100x^33+251x^34+124x^35+240x^36+632x^37+44x^38+432x^39+44x^40+92x^41+20x^42+20x^43+8x^44+8x^45+4x^46+1x^66

The gray image is a linear code over GF(2) with n=296, k=11 and d=128.
This code was found by Heurico 1.16 in 0.078 seconds.