The generator matrix

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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+153x^42+152x^43+439x^44+256x^45+842x^46+464x^47+857x^48+256x^49+374x^50+152x^51+94x^52+26x^54+9x^56+13x^58+7x^60+1x^72

The gray image is a linear code over GF(2) with n=376, k=12 and d=168.
This code was found by Heurico 1.16 in 0.344 seconds.