The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) 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 seconds.