The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1  X  1  X  0  X  1  1
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^3+X X^2+X X^2 X^3+X^2 X^2+X  X X^2 X^3+X^2+X X^2+X X^3 X^2  X X^3+X^2+X  0 X^3+X^2+X X^3  X  0 X^3+X  0 X^3+X^2+X X^3+X X^3+X^2 X^3+X X^3+X^2+X  X X^2 X^3+X^2 X^3 X^3+X^2 X^3+X X^3+X^2+X X^3+X^2+X X^3+X^2+X  X  X  0 X^3
 0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3 X^3+X^2 X^3  0 X^2 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2  0 X^2  0  0 X^3+X^2 X^3 X^3 X^2  0 X^2 X^3+X^2 X^3  0  0 X^2 X^2 X^3+X^2  0 X^3
 0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0  0 X^2 X^3 X^2 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3  0 X^2  0  0 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^2  0 X^2 X^2  0 X^2 X^3 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+124x^43+178x^44+168x^45+336x^46+456x^47+402x^48+160x^49+48x^50+92x^51+46x^52+24x^53+12x^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 35.7 seconds.