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  X  X  1  1  1  1  1 X^2  1  1  1  1  1 X^2  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2  0  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^2  0  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3+X^2 X^2 X^3+X^2 X^3 X^2  0 X^2 X^2 X^2  0 X^3+X^2  0 X^3 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3  0  0 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+85x^32+16x^33+108x^34+192x^35+338x^36+608x^37+344x^38+192x^39+56x^40+16x^41+44x^42+29x^44+16x^46+2x^48+1x^60

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.