The generator matrix

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

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+86x^40+218x^41+271x^42+518x^43+393x^44+478x^45+375x^46+456x^47+326x^48+360x^49+217x^50+190x^51+71x^52+62x^53+29x^54+20x^55+15x^56+2x^57+4x^58+4x^60

The gray image is a linear code over GF(2) with n=184, k=12 and d=80.
This code was found by Heurico 1.16 in 0.478 seconds.