The generator matrix

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

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+201x^28+8x^29+502x^30+96x^31+1130x^32+320x^33+1800x^34+1024x^35+2465x^36+1264x^37+2500x^38+864x^39+2002x^40+448x^41+968x^42+64x^43+545x^44+8x^45+118x^46+51x^48+4x^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 9.18 seconds.