The generator matrix

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

generates a code of length 37 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+65x^28+20x^29+46x^30+40x^31+144x^32+128x^33+387x^34+216x^35+907x^36+216x^37+907x^38+216x^39+370x^40+128x^41+122x^42+40x^43+43x^44+20x^45+61x^46+5x^48+11x^50+1x^52+1x^54+1x^62

The gray image is a linear code over GF(2) with n=148, k=12 and d=56.
This code was found by Heurico 1.16 in 0.617 seconds.