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  1  1  1  0  0  X X^2  0  1  0  X  0  1  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  0  X X^2 X^2+X X^2  X  0  X  0 X^2+X X^2  X  0  X  X X^2  X X^2+X X^2  0  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2  0  X X^2+X X^2+X X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  X  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  X X^2+X  0  0 X^2  0  0 X^2+X  X X^2 X^2  0  X  0 X^2+X X^2 X^2+X  0 X^2  X X^2  X  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  X X^2+X X^2 X^2  X  0 X^2+X  0 X^2+X X^2 X^2 X^2 X^2+X  X X^2+X  0 X^2 X^2+X  X X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  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+57x^28+66x^29+156x^30+206x^31+266x^32+412x^33+543x^34+772x^35+1034x^36+1126x^37+1044x^38+926x^39+542x^40+314x^41+227x^42+194x^43+133x^44+64x^45+72x^46+12x^47+15x^48+2x^49+5x^50+2x^51+1x^58

The gray image is a linear code over GF(2) with n=148, k=13 and d=56.
This code was found by Heurico 1.16 in 2.44 seconds.