The generator matrix

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

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+61x^34+104x^35+236x^36+274x^37+596x^38+500x^39+1061x^40+634x^41+1261x^42+724x^43+1030x^44+516x^45+574x^46+188x^47+205x^48+100x^49+61x^50+20x^51+22x^52+10x^53+6x^54+5x^56+2x^57+1x^58

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 2.24 seconds.