The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  0  1  1  1  0  1 X^3  1  X  X  1  X  1  X  1  1  1 X^2  1  X  1 X^3  1  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2  X X^3+X^2+X X^3+X X^2 X^3+X  X  0 X^3+X^2 X^2+X  X X^2+X  X X^3  X X^2 X^2 X^2+X  0 X^2 X^3 X^3+X^2+X  X X^3 X^2+X X^2+X X^3+X^2  X X^2+X X^2
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2  X X^2  X X^3+X^2+X X^3+X^2+X X^3+X  0 X^3 X^3+X^2+X X^3  X X^2 X^3 X^2 X^2 X^2 X^3+X^2+X X^3  X X^2+X  X  0  X X^2+X  0 X^3+X^2+X  X X^3+X^2+X X^2+X  X X^3+X^2 X^3+X  0
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^2  0 X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^2  0 X^3 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2 X^3  0 X^2 X^3 X^2

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+80x^41+265x^42+302x^43+542x^44+494x^45+879x^46+466x^47+507x^48+176x^49+155x^50+122x^51+70x^52+14x^53+8x^54+6x^55+4x^57+4x^58+1x^70

The gray image is a linear code over GF(2) with n=368, k=12 and d=164.
This code was found by Heurico 1.16 in 0.25 seconds.