The generator matrix

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

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+109x^42+230x^43+296x^44+478x^45+663x^46+702x^47+592x^48+422x^49+270x^50+146x^51+62x^52+58x^53+43x^54+10x^55+9x^56+2x^57+2x^58+1x^74

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 0.281 seconds.