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

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+52x^37+173x^38+208x^39+183x^40+380x^41+562x^42+584x^43+544x^44+816x^45+1087x^46+848x^47+687x^48+624x^49+596x^50+336x^51+96x^52+156x^53+115x^54+64x^55+21x^56+20x^57+26x^58+8x^59+1x^62+4x^64

The gray image is a linear code over GF(2) with n=184, k=13 and d=74.
This code was found by Heurico 1.16 in 16.1 seconds.