The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1  1  1  0  1  1 X^2 X^2+X  1  1  0  1  X  1  1  1 X^2+X  1 X^2  1 X^2  0  1  X  1 X^2
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+1  1 X^2+X X^2 X^2+X+1  1 X^2+X X+1  1  1  X X^2+1  1 X^2  1 X^2+X+1 X^2+1  0  1  0  1  1 X^2  1  1 X^2  0  1
 0  0  X X^2+X  0 X^2+X  X X^2+X  X  0 X^2  0  X X^2+X X^2  0 X^2  X  0 X^2+X  0  0 X^2+X  X  X X^2 X^2  0 X^2 X^2+X X^2+X  X X^2 X^2+X  X X^2 X^2+X
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2
 0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 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 29.

Homogenous weight enumerator: w(x)=1x^0+42x^29+100x^30+142x^31+306x^32+470x^33+631x^34+834x^35+1026x^36+1082x^37+1034x^38+926x^39+618x^40+418x^41+254x^42+134x^43+84x^44+36x^45+24x^46+12x^47+11x^48+3x^50+2x^52+2x^54

The gray image is a linear code over GF(2) with n=148, k=13 and d=58.
This code was found by Heurico 1.16 in 1.75 seconds.