The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+285x^42+842x^43+1367x^44+2094x^45+2386x^46+2718x^47+2355x^48+2022x^49+1145x^50+594x^51+331x^52+154x^53+56x^54+20x^55+4x^56+2x^57+4x^60+2x^63+2x^64

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 1.89 seconds.