The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  X  0  0  X  X X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X  2  0 X^2 X^2+X  X X^2  0  X X^2+X  0  X X^2+2  2 X^2+X X^2 X+2 X^2+X+2 X^2+2  2 X+2  2 X^2+X+2  2 X^2+2 X^2+X+2 X+2
 0  0  X  X X^2+2 X^2+X X^2+X+2 X^2 X^2 X^2+X X+2  2 X^2+X+2  2 X+2 X^2+2  X  2  X  X X^2+2 X^2+2 X^2+X+2 X^2+X  0 X^2 X+2 X^2+X+2  X X^2  0 X^2+X+2 X^2 X^2+2  2  X X+2  X X^2  0  0 X^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+242x^40+576x^42+184x^44+20x^48+1x^80

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 13.5 seconds.