The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  0  1  1 X^3+X^2+X  1 X^3+X^2  1  1  1  X  1  1  X  1  1 X^2+X X^3  1  1 X^2  0 X^2+X X^3+X^2+X  0 X^3+X^2 X^3+X  1  1 X^2+X X^3  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X+1  0  1 X^3+1 X^3+X^2+X  1 X^3+X^2  1 X+1 X^2+X X^3+X^2+1  1 X^2 X^3+1  1  0 X^2+1  1  1 X^3+X^2+X+1 X^3+X^2+X  1  1  1  1  1  1  1 X+1 X^3+X  1  1  X X^3+X^2+X X^2+1 X+1 X^2+X+1 X^3+X^2+1 X^2 X^2 X^3
 0  0 X^2  0  0 X^3  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0  0 X^3 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^2  0  0 X^3+X^2  0 X^3+X^2  0 X^3 X^3 X^3+X^2  0  0 X^2  0 X^3
 0  0  0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2  0 X^2  0 X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0  0  0  0  0 X^2 X^3 X^3 X^3 X^2  0 X^3+X^2 X^2  0  0 X^3+X^2 X^3+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+30x^42+178x^43+418x^44+508x^45+589x^46+696x^47+572x^48+492x^49+400x^50+162x^51+24x^52+4x^53+3x^54+4x^55+6x^56+4x^57+1x^58+2x^60+1x^64+1x^66

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 0.203 seconds.