The generator matrix

 1  0  1  1  1 X+2  1  1 3X  1  1 3X+2 X+2 2X+2  1  1  1  1 3X  1  1 X+2  1  1 2X+2  1  1  X  0  1  1  1  1  1  1  1  1 2X  0  2  1  X  1  1  1  2  1
 0  1  1 2X+2 X+1  1  X 2X+1  1 3X 3X+3  1  1  1 2X+2  3 3X X+1  1 2X X+3  1  X 2X+1  1  0 3X+3  1  1 2X+3 X+2 X+2 X+3 2X 2X+3  1 3X+1  1  1  1 2X+2  0 X+2 X+1 X+3  2 2X+2
 0  0  X 3X 2X 3X 3X 2X X+2  0  X  0  2 2X+2 X+2  2 X+2 2X+2  X  2 3X+2 X+2  2 3X+2  X 3X+2  2  0 X+2 X+2 2X+2  0 2X 3X  X  2 3X+2  2 3X 2X  2 3X X+2 X+2  0  X 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+214x^44+418x^45+320x^46+348x^47+186x^48+290x^49+146x^50+64x^51+42x^52+4x^54+12x^56+1x^58+1x^60+1x^62

The gray image is a code over GF(2) with n=376, k=11 and d=176.
This code was found by Heurico 1.16 in 0.094 seconds.