The generator matrix

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

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+274x^39+500x^40+848x^41+1198x^42+1190x^43+1538x^44+1784x^45+1776x^46+1762x^47+1589x^48+1344x^49+1069x^50+684x^51+386x^52+242x^53+111x^54+56x^55+18x^56+4x^57+5x^58+2x^59+2x^61+1x^62

The gray image is a linear code over GF(2) with n=184, k=14 and d=78.
This code was found by Heurico 1.13 in 223 seconds.