The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+3x^42+22x^43+3x^44+1x^46+2x^47

The gray image is a code over GF(2) with n=168, k=5 and d=84.
This code was found by Heurico 1.16 in 0.0213 seconds.