The generator matrix

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

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+184x^39+434x^40+344x^41+192x^42+320x^43+374x^44+160x^45+8x^47+21x^48+8x^49+2x^60

The gray image is a code over GF(2) with n=336, k=11 and d=156.
This code was found by Heurico 1.16 in 0.062 seconds.