The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  1  2  1  0  1  1  1  X  X X+2  1  1  X  1  1  2  1  0  1  1  X  1  1  1  1  1  1  1  1  X  2
 0  1  0  0  1  1  1  2  0  0  1  1  1  1  1  X  3  2  1  2  1 X+3  X  1 X+2 X+1  1 X+1  X  3 X+2  1  0  X X+3  1  1 X+3  X X+3  2  X
 0  0  1  1  2  3  1  1  0  1  2  2  3  3  1 X+3 X+3 X+2 X+3  1  0  0  3  0  3  1 X+3 X+2  1 X+2 X+2  1 X+1 X+2  3 X+3 X+1  0  X X+3  1  1
 0  0  0  X  0  X  X  X X+2  2  X X+2  0  2 X+2  X  2  0  2  0 X+2  2  0  0 X+2  0 X+2 X+2  2 X+2  2  2  X  X X+2 X+2  X  0 X+2  0  X X+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+352x^38+540x^40+468x^42+318x^44+220x^46+99x^48+44x^50+2x^52+4x^54

The gray image is a code over GF(2) with n=168, k=11 and d=76.
This code was found by Heurico 1.11 in 170 seconds.