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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+42x^38+70x^40+310x^42+48x^44+22x^46+8x^48+10x^50+1x^80

The gray image is a code over GF(2) with n=168, k=9 and d=76.
This code was found by Heurico 1.16 in 7.57 seconds.