The generator matrix

 1  0  0  1  1  1  0  1  2  1  1  2  1  2 X+2  1  1 X+2 X+2  X  1  1  1  1  1  0  1  X  1  1  X X+2  1  0  2  1  1  1  2  1  X  1
 0  1  0  0  1  3  1  X  1  1  2  1 X+1 X+2  1 X+2 X+3  1  X  1 X+2 X+1  1  2 X+3  1  1  2  X  2  1  1  2  1  1  X  0  1  1 X+2  1  2
 0  0  1 X+1 X+3  0 X+1  1  X  1  X  3  0  1  X  2 X+2 X+3  1  2  3 X+3 X+3 X+1 X+2 X+2 X+2  1 X+2  3  3 X+2  X  3  2  3  X X+2  0 X+3  3 X+1
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  2  2  0  2  0  2  2  2  0  0  0  2  2  2  2  2  0  2  2  2
 0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  0  0  0  2  0  2  0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  0  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+335x^38+552x^40+512x^42+267x^44+232x^46+102x^48+36x^50+5x^52+5x^54+1x^56

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 3.19 seconds.