The generator matrix

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

generates a code of length 43 over Z4[X]/(X^3+2,2X) 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.