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

generates a code of length 47 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+136x^43+182x^44+160x^45+320x^46+448x^47+406x^48+144x^49+64x^50+120x^51+42x^52+16x^53+8x^56+1x^80

The gray image is a code over GF(2) with n=376, k=11 and d=172.
This code was found by Heurico 1.16 in 73.6 seconds.