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 2X+2  X
 0  2  0  0  0 2X+2  2 2X+2  0  0  0  0 2X+2  2 2X+2  2  0 2X  2 2X  0 2X+2  2 2X+2 2X  2 2X 2X+2  0 2X  2 2X+2 2X 2X+2  0 2X+2 2X+2 2X 2X 2X+2  2 2X  0 2X+2 2X+2 2X  2
 0  0  2  0 2X+2 2X+2  2  0  0  0 2X+2  2 2X+2  2  0  0 2X  0  2 2X+2 2X+2 2X 2X+2 2X  0 2X 2X  0  2 2X+2 2X+2  2 2X  2  2  2 2X  2 2X 2X  0 2X 2X  0 2X+2  0 2X+2
 0  0  0  2 2X+2  0  2 2X+2 2X 2X+2  2 2X 2X 2X+2  2 2X 2X 2X+2  0  2 2X  0  2  2  0 2X+2  2 2X 2X+2  0  0 2X+2 2X+2  0  2  2 2X+2 2X+2  0 2X 2X+2 2X  0  0 2X 2X+2 2X+2

generates a code of length 47 over Z4[X]/(X^2+2X+2) 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 code over GF(2) with n=376, k=10 and d=176.
This code was found by Heurico 1.16 in 0.359 seconds.