The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+358x^40+320x^42+336x^44+6x^48+2x^56+1x^64

The gray image is a code over GF(2) with n=336, k=10 and d=160.
This code was found by Heurico 1.16 in 11.1 seconds.