The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  1  X  0  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  2  0  1  1  1  X  1  2  1 X^2+2  1
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  0  2 X^2+X X^2+X X^2+2 X^2+2  X X+2 X^2+X  X X^2+X X^2+X+2  X  0  2 X^2+X X^2+2 X^2+X X+2  X X+2 X^2  0 X^2+2  0 X^2+2 X+2 X^2+X  X  X  X  X X^2+X+2 X^2+X+2  X  X X^2+X+2  X  0
 0  0 X^2+2  0 X^2  0  2  0 X^2  0 X^2 X^2+2 X^2+2  2 X^2+2 X^2  0  0  2 X^2 X^2+2 X^2  2 X^2+2 X^2 X^2+2  0  2 X^2 X^2+2  2  2 X^2+2  2  0 X^2+2 X^2+2 X^2+2 X^2 X^2  0  0 X^2+2  2  0 X^2+2  0
 0  0  0 X^2+2  0  2  2 X^2 X^2 X^2 X^2+2  0 X^2 X^2+2  0 X^2+2  2 X^2+2  2  0 X^2+2 X^2 X^2+2 X^2+2 X^2+2  0  0 X^2  0  2  2  2  0 X^2+2  2 X^2  2 X^2+2  2 X^2 X^2 X^2  2  0  0 X^2  0
 0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  0  0  2  0  0  2  2  0  2  0  2  2  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  2  2  2  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+153x^42+152x^43+439x^44+256x^45+842x^46+464x^47+857x^48+256x^49+374x^50+152x^51+94x^52+26x^54+9x^56+13x^58+7x^60+1x^72

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 0.328 seconds.