The generator matrix

 1  0  0  1  1  1  X  2  1  0  1  1  1  2  1  1  2 X+2  1  X  1  0  1  1  1  1  1  1  1  1  1  0  1  2  1  1 X+2  0  1  X  1  1
 0  1  0  1  0 X+3  1  X X+1  1  X  3  X  1  1  2  0  1  2  1  3  1  2  X  0 X+3 X+1  3  3  2  1  1 X+3  0 X+3 X+1  1  1 X+1  1 X+2  2
 0  0  1  1  1  0  1  1 X+3 X+2 X+1 X+2  X X+1  X  3  1 X+2  0 X+3  2  X X+3  0 X+3  X X+3  X X+3 X+3  2  3 X+1  1  1 X+1  2  1 X+1 X+2 X+3  0
 0  0  0  X  0 X+2  2  X  0 X+2 X+2  0 X+2  2  0  2 X+2  X  X X+2 X+2  2  X  0  2  0  2  0  0 X+2  2  0  X  0  X  2 X+2 X+2  X  0  2  0
 0  0  0  0  X  0  2 X+2 X+2  X  2 X+2  X X+2  0  0  0  2  2  0 X+2  X  X  X X+2  2 X+2  X  0  0  2  2  X X+2  X  0  0  2  0  X  0  X
 0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0  0  2  0  0  2  2  2  2  0  0  2  2  0  0  0  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+76x^34+188x^35+427x^36+712x^37+997x^38+1328x^39+1558x^40+1870x^41+1982x^42+1958x^43+1804x^44+1266x^45+857x^46+614x^47+357x^48+210x^49+112x^50+38x^51+13x^52+6x^53+5x^54+2x^55+2x^58+1x^62

The gray image is a code over GF(2) with n=168, k=14 and d=68.
This code was found by Heurico 1.16 in 6.67 seconds.