The generator matrix

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

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+136x^43+182x^44+160x^45+320x^46+448x^47+406x^48+144x^49+64x^50+120x^51+42x^52+16x^53+8x^56+1x^80

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 74.4 seconds.