The generator matrix

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

generates a code of length 49 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+216x^42+1194x^43+3131x^44+5912x^45+10249x^46+14886x^47+19047x^48+21426x^49+19494x^50+15406x^51+10203x^52+5462x^53+2777x^54+1060x^55+382x^56+174x^57+30x^58+12x^59+4x^60+2x^61+2x^63+2x^66

The gray image is a code over GF(2) with n=392, k=17 and d=168.
This code was found by Heurico 1.16 in 93.7 seconds.