The generator matrix

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

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+224x^34+60x^35+673x^36+324x^37+1188x^38+1000x^39+1900x^40+1732x^41+2294x^42+1632x^43+1958x^44+972x^45+1152x^46+376x^47+562x^48+44x^49+206x^50+4x^51+56x^52+24x^54+1x^56+1x^60

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 14.9 seconds.