The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  2  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X X^2+2 X+2  2  X X^2+2 X^2+X+2  X  0 X^2+2 X^2+X X^2+X  2 X^2 X+2 X+2 X^2+X  0 X^2+X  0 X^2+2 X^2+2  X X^2+X+2  2  2 X^2+2 X^2+X+2 X^2  0 X^2+X X^2 X+2
 0  0 X^2+2  0 X^2+2 X^2  0 X^2  2  2  2  2 X^2 X^2+2 X^2 X^2+2 X^2  0  0  0 X^2+2 X^2 X^2  2 X^2+2 X^2  2  2 X^2+2 X^2+2  2  2 X^2  2 X^2+2 X^2  2  0 X^2 X^2+2 X^2 X^2
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  0  0  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  0  2  0  0  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+72x^39+52x^40+264x^41+296x^42+232x^43+20x^44+56x^45+8x^46+16x^47+6x^48+1x^80

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 28.4 seconds.