The generator matrix

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

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+260x^39+337x^40+340x^41+281x^42+340x^43+214x^44+156x^45+54x^46+48x^47+6x^48+1x^50+8x^51+2x^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 93.4 seconds.