The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  1  1  2  X  X  X  0  1  1  X  2  X  1  1  1  1  1  1  1  1  2  1  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2  X X+3  1  1  1  0 X+2  X  0  2  X  X  2 X+1  3 X+3  1  0  2 X+2 X+2  2 X+1 X+3
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  2  2  0  0  0  0  2  0  0  2  2  0  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+72x^42+38x^44+14x^46+2x^54+1x^56

The gray image is a code over GF(2) with n=172, k=7 and d=84.
This code was found by Heurico 1.16 in 0.0241 seconds.