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

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+34x^33+42x^34+28x^35+282x^36+272x^37+280x^38+20x^39+19x^40+14x^41+14x^42+16x^43+1x^44+1x^68

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 0.047 seconds.