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

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+66x^40+128x^42+56x^44+4x^48+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 0.0329 seconds.