The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X X^2  X X^2 X^2  X  0  0  1  0 X^2  1  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X  X X^2  X X^2 X^2 X^2+X X^2  X  X X^2  0 X^2 X^2+X  0 X^2  X  X X^2 X^2  X  X X^2+X X^2+X
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X X^2+X X^2  X  X X^2+X X^2 X^2+X  0 X^2+X X^2 X^2  0  X  X  0 X^2+X X^2  0  0  0  0  X X^2
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X X^2+X  0 X^2+X X^2+X  0 X^2 X^2 X^2+X X^2  X  X  X  X  0 X^2  X X^2+X  X  X  0 X^2
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X X^2  0  X  X X^2 X^2+X X^2+X  0  0 X^2+X  X  0 X^2  X X^2 X^2 X^2+X  X X^2 X^2+X  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0  0
 0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0  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+192x^28+4x^29+546x^30+56x^31+1011x^32+320x^33+1700x^34+968x^35+2690x^36+1400x^37+2638x^38+968x^39+1838x^40+320x^41+978x^42+56x^43+492x^44+4x^45+152x^46+46x^48+2x^50+1x^52+1x^68

The gray image is a linear code over GF(2) with n=148, k=14 and d=56.
This code was found by Heurico 1.16 in 9.28 seconds.