The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^42+44x^43+6x^44+1x^46+4x^47+1x^48+1x^62

The gray image is a code over GF(2) with n=172, k=6 and d=84.
This code was found by Heurico 1.16 in 0.0314 seconds.