The generator matrix

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

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+109x^36+64x^37+64x^38+15x^40+1x^44+2x^52

The gray image is a linear code over GF(2) with n=296, k=8 and d=144.
This code was found by Heurico 1.16 in 0.078 seconds.