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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+64x^44+56x^45+156x^46+464x^47+165x^48+56x^49+60x^50+1x^52+1x^92

The gray image is a linear code over GF(2) with n=376, k=10 and d=176.
This code was found by Heurico 1.16 in 0.062 seconds.