The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+334x^42+808x^43+1293x^44+1264x^45+1374x^46+1024x^47+868x^48+560x^49+362x^50+152x^51+91x^52+32x^53+26x^54+3x^56

The gray image is a linear code over GF(2) with n=368, k=13 and d=168.
This code was found by Heurico 1.16 in 1.7 seconds.