The generator matrix

 1  0  0  1  1  1 X^3  1  1 X^3+X^2+X  1 X^3  0  1 X^3  1  1  X  1  1  X  1  1  1 X^3+X X^3+X^2+X  1 X^2+X X^2  1  1  1  1  1  1 X^2  1 X^2+X X^3+X X^2  1  1  1  0  1  1  1
 0  1  0  0 X^3+X^2+1 X^3+X^2+1  1  X X^3+X+1 X^3 X^3  1  1 X^2+1 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+1  1 X^2+X X^2  1 X^3+X+1  1 X^3+X  1  1 X^3+X  1 X^3+X^2 X^3+1 X^3+X X^2 X+1  1 X^2+X+1  1 X^2+X+1 X^3+X  1  1  X X^3+X+1 X^3+X^2+X+1 X^3 X^3+X^2+X X^3+1 X^2
 0  0  1 X+1 X+1 X^2 X+1 X^3+X^2+1 X^3+X+1  1  X  X X^3+X^2+1 X^3+X  1  X X^3+X^2+1 X+1 X^2  1 X^3+X^2+X X^3+1 X^3 X^2+X  1  0 X^3+X^2+X+1 X^3  1  X X^2+X+1  0 X^3+1 X^2 X^3+X^2+X X^3+X^2+X+1 X^3  1  0 X^3+X+1 X^3+X X+1 X^2  1 X^2+1 X^3+X^2 X+1
 0  0  0 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2  0  0 X^2 X^3 X^3 X^3+X^2  0 X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^2 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+256x^42+778x^43+1433x^44+2258x^45+2365x^46+2614x^47+2301x^48+1988x^49+1222x^50+650x^51+275x^52+122x^53+57x^54+34x^55+20x^56+4x^58+4x^59+2x^60

The gray image is a linear code over GF(2) with n=376, k=14 and d=168.
This code was found by Heurico 1.16 in 3.25 seconds.