The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+78x^40+96x^42+80x^44+1x^80

The gray image is a code over GF(2) with n=168, k=8 and d=80.
This code was found by Heurico 1.16 in 0.0324 seconds.