The generator matrix

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

generates a code of length 43 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+144x^42+86x^44+22x^46+2x^54+1x^56

The gray image is a code over GF(2) with n=344, k=8 and d=168.
This code was found by Heurico 1.16 in 0.047 seconds.