The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+67x^34+86x^35+279x^36+270x^37+678x^38+532x^39+915x^40+652x^41+1239x^42+690x^43+995x^44+516x^45+617x^46+202x^47+204x^48+92x^49+82x^50+24x^51+34x^52+6x^53+5x^54+2x^55+4x^56

The gray image is a code over GF(2) with n=168, k=13 and d=68.
This code was found by Heurico 1.16 in 2.38 seconds.