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  1 X^3  1  1  1  X  X  1  1  0  1  1 X^3 X^2  1  1  1
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2 X^2+X X^2+X  0 X^3+X X^3+X^2+X X^2 X^3+X^2+X X^3+X X^3 X^3+X^2+X X^3+X^2  0  X X^2 X^3+X^2+X X^3+X X^2  X  X X^3 X^3+X^2+X X^2+X  0 X^3+X^2 X^3+X  X X^3+X^2+X X^3  X X^2 X^3 X^2+X X^3
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3  X X^3+X  0 X^2+X X^3+X^2+X X^3+X^2  0 X^3+X^2+X X^2 X^3 X^3 X^3+X^2  X X^2+X X^2 X^2 X^3 X^3+X X^3+X X^3+X^2+X X^2+X  X X^3+X X^2+X X^2  0 X^3+X X^3+X X^3+X X^2+X X^3+X^2+X X^3+X^2+X X^2  X  0  X X^3+X
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  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+138x^43+108x^44+252x^45+343x^46+440x^47+338x^48+188x^49+94x^50+78x^51+8x^52+40x^53+3x^54+16x^55+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 0.109 seconds.