The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  0  1  1  1  X  1  0  1  0  X  X  1  1  X  1  1
 0  X  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  2  X  0  0  0  2  0 X+2  X X+2  X X+2  X  X X+2  2 X+2 X+2  X X+2  X X+2 X+2  0  2 X+2  0  0
 0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  2  0  2  0  2  0  0  0  0  2  0  0  2  2  0  2  2  2  2  0  2  0
 0  0  0  2  0  0  0  0  0  0  0  2  0  2  0  2  2  2  2  2  2  0  2  2  0  0  2  0  2  2  0  2  2  0  0  0  2  0  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  2  0  2  0  2  0  2  0  0  2  2  2  0  2  2  0  2  2  2  2  0  0  0  2  2  2  2  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  0  2  2  2  2  2  0  2  0  2  2  2  0  2  0  2  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  0  0  0  2  2
 0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  0  0  2  0  2  0  0  2  2  0  0  2  2  2  2  0  0  2  0  2  2  2  2  2  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+30x^34+113x^36+224x^38+405x^40+529x^42+399x^44+208x^46+92x^48+24x^50+7x^52+8x^54+5x^56+1x^58+1x^60+1x^64

The gray image is a code over GF(2) with n=168, k=11 and d=68.
This code was found by Heurico 1.16 in 0.226 seconds.