The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  2  1  1  X  1  X  1  X  1  1  1  1  1  1  X  1  0  1  1  1  X  1
 0  1 X+1 X+2  1  1 X+1  0  1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  3  1  0  0 X+2  2  2  X  X  X  2  2 X+2 X+1  X X+3  3  1  0  0
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  2  2  2  0  0  2  2  0  2  2  0  0  2  0  0  2  2  2  2  2  2  0
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  2  0  2  0  2  0  0  0  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  2  2  0  2  2  0  0  2  0  0  2  0  2  0  2  2  0  2  2  0  0  2  0  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+15x^38+86x^39+37x^40+126x^41+42x^42+92x^43+18x^44+60x^45+1x^46+14x^47+5x^48+6x^49+5x^50+2x^52+1x^58+1x^72

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 0.0309 seconds.