The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+456x^39+686x^40+838x^41+685x^42+436x^43+338x^44+326x^45+169x^46+136x^47+6x^48+16x^49+2x^50+1x^52

The gray image is a code over GF(2) with n=336, k=12 and d=156.
This code was found by Heurico 1.16 in 0.125 seconds.