The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  X  1 X^2+2  1  1  1  1 X^2+X+2  1  0  1  1 X^2+X  1 X^2  1 X+2  1 X^2  1  0 X^2+X+2  1  1 X^2+2  1  X  1  1 X+2  1 X^2+2 X^2  0
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+3 X^2+2  1  X  1 X^2+X+1  3 X+1  0  1 X^2+X+2  1 X+1  2  1 X+2  1 X^2  1 X^2+X+2  1 X+3  1  1 X^2+3 X^2+3  1 X^2 X^2+2  0 X^2+1  1 X^2+X+1  X  0 X^2
 0  0 X^2  0  0  0  0  2  2  2  2 X^2  2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2  2  2  0  2  2  0  2 X^2 X^2+2  2 X^2 X^2  0 X^2 X^2+2  0  0 X^2+2 X^2
 0  0  0 X^2+2  2 X^2+2 X^2  2 X^2 X^2  2  2  0 X^2 X^2+2  2  0 X^2 X^2+2  2 X^2 X^2  2 X^2+2  2  0 X^2+2 X^2+2 X^2  0  0 X^2 X^2 X^2 X^2 X^2+2 X^2  2 X^2 X^2+2 X^2+2  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+336x^38+256x^39+625x^40+504x^41+710x^42+552x^43+581x^44+200x^45+222x^46+24x^47+64x^48+10x^50+7x^52+2x^54+2x^56

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 2.8 seconds.