The generator matrix

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

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+30x^42+178x^43+418x^44+508x^45+589x^46+696x^47+572x^48+492x^49+400x^50+162x^51+24x^52+4x^53+3x^54+4x^55+6x^56+4x^57+1x^58+2x^60+1x^64+1x^66

The gray image is a code over GF(2) with n=376, k=12 and d=168.
This code was found by Heurico 1.16 in 0.203 seconds.