The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X  2  0  X  1  X  1  0  1  1  X  0  1  1  0  X  X  X
 0  X  0  0  0  0  0  0  0  X X+2  X  2  2  X  0  2  X X+2  2  X X+2  X  0  X  0  X  X  2  2 X+2  X  X  0  2  X X+2 X+2  X  2  0  0
 0  0  X  0  0  0  X X+2  X  X  X  0  0  X  2  X  2  X X+2  2 X+2  0 X+2  X  2  2  2  2 X+2  2  X  2  0  2  0  0  2  X  2  2  2  X
 0  0  0  X  0  X  X  X  2  0  0  2  2  2 X+2 X+2  2 X+2 X+2 X+2  X  X  0  2  X  X  0 X+2  2  0  X  0  0 X+2 X+2  0  X X+2  X  0  2  X
 0  0  0  0  X  X  2 X+2 X+2  0  X  X  0 X+2  X  2  X  X  2 X+2  0  0  2  0  2 X+2  2  0  X X+2  0 X+2 X+2  0 X+2  2  X  X X+2 X+2 X+2  0
 0  0  0  0  0  2  2  2  2  2  0  0  2  0  2  0  2  0  0  0  2  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  0  2  2  0  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+48x^34+88x^35+130x^36+194x^37+221x^38+360x^39+395x^40+420x^41+492x^42+410x^43+366x^44+288x^45+208x^46+166x^47+119x^48+76x^49+48x^50+30x^51+12x^52+14x^53+7x^54+2x^55+1x^56

The gray image is a code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 0.687 seconds.