The generator matrix

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

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+239x^38+770x^39+1365x^40+1360x^41+1325x^42+1048x^43+926x^44+540x^45+367x^46+154x^47+59x^48+28x^49+5x^50+4x^51+1x^56

The gray image is a code over GF(2) with n=336, k=13 and d=152.
This code was found by Heurico 1.16 in 0.407 seconds.