The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+16x^37+3x^38+8x^39+3x^40+1x^46

The gray image is a linear code over GF(2) with n=148, k=5 and d=74.
This code was found by Heurico 1.16 in 0.0133 seconds.