The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 2X  1
 0  X  0 3X+2 2X+2 X+2  2  X  0 3X+2  2 3X 2X  X  2 X+2  X  0  2 3X+2 3X+2 2X 2X+2 3X 3X 3X+2  0 3X+2  0  2  2  X X+2 2X 2X  2 X+2 2X+2  0 3X+2 2X+2 3X
 0  0  2  0  2 2X+2  0 2X+2 2X 2X 2X 2X 2X+2  2 2X+2  2 2X+2  0  0  0  2 2X+2 2X+2 2X  2 2X+2 2X 2X  2  2 2X 2X 2X+2 2X  2 2X+2 2X  0 2X+2  2 2X+2 2X+2
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X  0  0 2X  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+72x^39+52x^40+264x^41+296x^42+232x^43+20x^44+56x^45+8x^46+16x^47+6x^48+1x^80

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 28.5 seconds.