The generator matrix

 1  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  X  1  1  1  1  1  1  1 X^3  1  1  1  X  1  0  1  1  X X^2  1  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^2 X^3  0 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^2  0 X^3  0 X^2 X^2  0 X^3+X^2  0 X^2 X^3+X^2 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3  0  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3  0  0 X^3+X^2 X^3+X^2 X^3  0 X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2 X^2  0  0 X^3 X^2 X^3 X^3 X^2  0 X^3+X^2 X^2 X^2 X^3  0  0 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0  0 X^2 X^3  0 X^2 X^3+X^2  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  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 42.

Homogenous weight enumerator: w(x)=1x^0+102x^42+164x^44+96x^45+554x^46+320x^47+488x^48+96x^49+114x^50+44x^52+54x^54+6x^56+8x^58+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 0.188 seconds.