The generator matrix

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

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+520x^44+664x^45+884x^46+472x^47+624x^48+296x^49+288x^50+136x^51+136x^52+32x^53+36x^54+5x^56+2x^60

The gray image is a code over GF(2) with n=376, k=12 and d=176.
This code was found by Heurico 1.16 in 1.66 seconds.