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

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+105x^44+272x^46+256x^47+330x^48+16x^50+43x^52+1x^88

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 0.375 seconds.