The generator matrix

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

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+92x^43+171x^44+258x^45+407x^46+342x^47+349x^48+154x^49+120x^50+58x^51+23x^52+52x^53+16x^54+4x^55+1x^78

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 0.125 seconds.