The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1  X  1  2  1  1  1 X+2  1  1  0  X  1  X  1  1  1  X  1 X+2  1  1 X+2  1  0  1  1  1 X+2  1  0  1
 0  1  0  0  3 X+1  1  2  0  0 X+3  1  1  1  3  X X+2  1  3 X+3 X+2  1  2  X  2  2  1  1  1  1  0  3  1  3  1  X  X X+2  1  X  1 X+3
 0  0  1  1  3  2  3  1  2 X+1 X+3  2  2  1  1 X+2  3  2  1  0  1 X+1  X  1 X+2  3 X+3  1  X X+3  3  X  X X+3 X+2  X  0 X+1 X+1 X+2  2  X
 0  0  0  X  X  0  X  X X+2  2  0 X+2  X  2 X+2  0  0  2  0  X  2  X X+2  X  0  2 X+2  2  X  0  0  0  2  2  X X+2  2 X+2 X+2 X+2  X  0

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+360x^38+516x^40+506x^42+286x^44+214x^46+123x^48+38x^50+2x^52+2x^54

The gray image is a code over GF(2) with n=168, k=11 and d=76.
This code was found by Heurico 1.16 in 37.4 seconds.