The generator matrix

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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+96x^43+243x^44+152x^45+440x^46+160x^47+516x^48+144x^49+184x^50+64x^51+21x^52+24x^53+1x^56+2x^64

The gray image is a linear code over GF(2) with n=376, k=11 and d=172.
This code was found by Heurico 1.16 in 0.094 seconds.