The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+28x^38+3x^40

The gray image is a linear code over GF(2) with n=296, k=5 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.