The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  X  1 X^2+2  1 X^2+X  1  1 X+2  1  X  1  1  1 X^2+2 X^2  1  1  1  1  1  1 X^2  1  1  1  2 X^2  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2  3  1 X+2 X+3  1 X^2+1  1 X^2+X+2  1 X^2+2 X^2+X+3  1 X^2+1  1  3 X+1  X  1  1  3 X+1  0  2 X^2+X X^2+X+1  1 X^2+X+1 X^2+3 X+3  1  1 X+3  3 X+1 X^2+2
 0  0  X  0 X+2  X X+2  2  0 X^2+X+2 X^2  X X^2 X^2 X+2 X^2+2 X^2+X  2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+X+2  X X^2+2 X^2+X X+2  2 X^2+X  X X^2+X  0 X^2+X+2  X  X X^2+2  2  0 X+2 X^2+X+2
 0  0  0  2  0  2  2  2  2  0  0  2  2  0  0  2  0  2  0  0  0  2  2  0  0  2  0  0  0  2  2  0  2  0  0  2  2  2  0  0  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+135x^38+380x^39+593x^40+690x^41+583x^42+672x^43+544x^44+356x^45+88x^46+8x^47+18x^48+2x^49+8x^50+4x^51+12x^52+1x^58+1x^62

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 0.172 seconds.