The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1 X^2  1  1  X  1  1  1  1 X^2+X+2  1  1  1  1  1  0  1  0 X^2+2  1  1  2  0  1 X^2  X  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3  1 X^2+1  2  1  X X+1 X^2+X X+3  1 X^2+X+1  1  1 X^2+X+1 X+2  X X^2+X+2  1  1  2 X^2+2  1 X^2+2  2  1  1 X^2+X
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X+2 X^2+X+2 X^2+2 X^2+X+2 X^2+2 X^2+X+2 X^2+X X^2  X X^2+X X^2 X^2+X X^2+2 X^2+X+2 X^2 X^2 X^2+X+2 X^2+2 X^2+X+2 X^2+2 X^2+2  X X^2+X X^2+X+2 X^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+204x^39+338x^40+428x^41+274x^42+328x^43+226x^44+156x^45+50x^46+16x^47+12x^49+4x^50+4x^51+2x^52+4x^53+1x^56

The gray image is a code over GF(2) with n=336, k=11 and d=156.
This code was found by Heurico 1.16 in 0.046 seconds.