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  1  1  1  1  1  X  1
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^3  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^2 X^2  0 X^2 X^3 X^2  0 X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3+X^2 X^2 X^3+X^2  0 X^2  0 X^3 X^3+X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2 X^3  0 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^2 X^3  0 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+32x^33+36x^34+28x^35+94x^36+652x^37+92x^38+28x^39+24x^40+20x^41+8x^42+8x^43+1x^72

The gray image is a linear code over GF(2) with n=296, k=10 and d=132.
This code was found by Heurico 1.16 in 0.046 seconds.