The generator matrix

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

generates a code of length 47 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+243x^42+804x^43+1660x^44+1852x^45+2493x^46+2498x^47+2607x^48+1802x^49+1267x^50+556x^51+364x^52+132x^53+59x^54+30x^55+8x^56+6x^57+2x^58

The gray image is a code over GF(2) with n=376, k=14 and d=168.
This code was found by Heurico 1.16 in 1.83 seconds.