The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+452x^39+618x^40+920x^41+637x^42+560x^43+330x^44+276x^45+122x^46+120x^47+17x^48+36x^49+1x^50+4x^51+2x^52

The gray image is a code over GF(2) with n=336, k=12 and d=156.
This code was found by Heurico 1.16 in 0.921 seconds.