The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^42+44x^43+6x^44+4x^47+1x^48+2x^54

The gray image is a code over GF(2) with n=344, k=6 and d=168.
This code was found by Heurico 1.16 in 0.031 seconds.