The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+271x^38+232x^39+608x^40+544x^41+845x^42+528x^43+577x^44+224x^45+217x^46+8x^47+27x^48+3x^50+2x^52+8x^54+1x^60

The gray image is a code over GF(2) with n=336, k=12 and d=152.
This code was found by Heurico 1.16 in 0.953 seconds.