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

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+124x^42+161x^44+64x^45+496x^46+384x^47+500x^48+64x^49+160x^50+30x^52+48x^54+10x^56+4x^58+1x^60+1x^80

The gray image is a linear code over GF(2) with n=376, k=11 and d=168.
This code was found by Heurico 1.16 in 69.6 seconds.