The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^42+9x^44+2x^46+1x^48+1x^52

The gray image is a code over GF(2) with n=336, k=6 and d=168.
This code was found by Heurico 1.16 in 0.031 seconds.