The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+34x^39+262x^40+172x^41+237x^42+50x^43+143x^44+48x^45+51x^46+16x^47+8x^48+1x^52+1x^60

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 0.047 seconds.