The generator matrix

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

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+34x^39+262x^40+172x^41+237x^42+50x^43+143x^44+48x^45+51x^46+16x^47+8x^48+1x^52+1x^60

The gray image is a code over GF(2) with n=336, k=10 and d=156.
This code was found by Heurico 1.16 in 0.047 seconds.