The generator matrix

 1  0  1  1  1  2  X  1  1  1 X+2  1  1  1  1  1  1  1  1  1  0  0 X+2 X+2  0  0  2  X  X  0  2  0  0 X+2  1  1  1  1  2  X  1  1
 0  1  1 X+2 X+3  1  1  2  3 X+1  1  2 X+2  2  X X+2 X+1  3 X+1  3  1  1  1  1  1  1  X  1  1  1  1  1  1  1  2  3 X+1 X+3  0  1 X+1  X
 0  0  X  0 X+2  X  X  X  2  2  0 X+2  0  2  X  X  0  2 X+2 X+2  0 X+2  X  2  0  2  X  X X+2 X+2  2  X  0  0 X+2  X  0  2  X  0  X  X
 0  0  0  2  0  2  2  0  2  2  0  0  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  2  0  2  2  2  2  2  2  2  0  2  0
 0  0  0  0  2  2  0  2  0  2  2  0  2  2  2  0  0  2  0  2  2  0  2  0  2  2  2  0  0  2  0  2  0  2  0  0  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 38.

Homogenous weight enumerator: w(x)=1x^0+172x^38+243x^40+274x^42+147x^44+136x^46+23x^48+26x^50+1x^56+1x^60

The gray image is a code over GF(2) with n=168, k=10 and d=76.
This code was found by Heurico 1.16 in 0.305 seconds.