The generator matrix

 1  0  0  1  1  1  0  1 X+2  1  2  1  X  1  1  X  1 X+2  2  1  1  1  1  X  1  X X+2  1  2  X  1  1  X  1  2  1  1  1  1  1  X  1
 0  1  0  1  X X+3  1  2  0  X  1 X+3  1 X+1 X+2  1 X+1  1 X+2 X+3  2  0 X+3  1  X  0  1  3 X+2  1  X X+2 X+2 X+1  1 X+1  2 X+1 X+3 X+2  X  1
 0  0  1  1  1  0 X+3  X  1 X+3  X X+1 X+3  X  1  X  3 X+1  1  1  0  3  0  2  2  1  X X+2  1 X+2  0 X+1  1  X  1  1 X+3  3  2  2  0  1
 0  0  0  X  0 X+2 X+2  0  0  0  2  X  X X+2  X  0 X+2  2 X+2  0  X  X  2  X X+2 X+2 X+2 X+2  2 X+2 X+2 X+2  2  2  X  X  0  2 X+2  X X+2  0
 0  0  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  2  2  2  2  2  0
 0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  2  2  0  0  0  0  0  2  0  2  2  0  2  2  2  2  2  0  2  0
 0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  2  2  2  0  2  0  0  2  2  2  0  0  2  0  0  0  0  0  2  2  2  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+74x^34+254x^35+396x^36+736x^37+999x^38+1268x^39+1612x^40+1778x^41+2027x^42+1924x^43+1702x^44+1366x^45+900x^46+612x^47+359x^48+190x^49+90x^50+38x^51+22x^52+26x^53+5x^54+4x^56+1x^58

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 6.88 seconds.