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

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+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 13.2 seconds.