The generator matrix

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

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+216x^42+860x^43+1464x^44+2066x^45+2506x^46+2652x^47+2271x^48+1928x^49+1221x^50+634x^51+312x^52+146x^53+64x^54+26x^55+8x^56+4x^57+1x^58+2x^59+2x^63

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 1.75 seconds.