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

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+64x^44+56x^45+156x^46+464x^47+165x^48+56x^49+60x^50+1x^52+1x^92

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 0.062 seconds.