The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  X  1  1  X  X  1  1  1  1  2  1  1  1  X X^2  1  X  1  X
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+2 X^2+X+2  X X^2+2 X^2+X+2  X X+2 X^2 X+2  X  0  0 X^2+X+2 X^2  2  X X^2+2 X+2 X^2 X^2+X+2  X  2 X^2+X+2 X^2+X+2  X X^2  2 X^2+X  X  X  X X+2 X^2+X+2 X^2
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2  X X^2  X X^2+X+2 X+2 X^2+X+2  0  2 X^2+X+2  2  X X+2 X^2+2 X^2+2  2  2  X  2 X+2  X X^2+2 X^2+2 X^2+X+2 X+2 X^2+X  X  2 X^2+X+2 X^2 X^2 X^2 X^2 X^2+X  0
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0 X^2+2  0  2 X^2 X^2  0 X^2 X^2+2  0  0  2 X^2+2  2  2  2 X^2  0  2 X^2+2  0  2 X^2+2  0  0 X^2+2  2 X^2 X^2+2  2  2  0 X^2+2  0 X^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+109x^42+230x^43+296x^44+478x^45+663x^46+702x^47+592x^48+422x^49+270x^50+146x^51+62x^52+58x^53+43x^54+10x^55+9x^56+2x^57+2x^58+1x^74

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 0.265 seconds.