The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+558x^43+581x^44+956x^45+382x^46+664x^47+317x^48+328x^49+102x^50+150x^51+21x^52+28x^53+2x^54+4x^55+2x^58

The gray image is a linear code over GF(2) with n=368, k=12 and d=172.
This code was found by Heurico 1.16 in 0.812 seconds.