The generator matrix

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

generates a code of length 37 over Z2[X]/(X^4) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+6x^36+110x^37+6x^38+1x^40+1x^42+2x^45+1x^50

The gray image is a linear code over GF(2) with n=296, k=7 and d=144.
This code was found by Heurico 1.16 in 0.032 seconds.