The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0  0  X  1  X  0  X  1  2  2  2  1  X  1  2  2  X  0  1
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  2  2  0 X+2  0 X+2  2  0  X  X X+2  0  0  0  2  2  X  X  X X+2  X  X  X  X  0  X  0
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2  X  X  X  2  0  0  X X+2  0  2  0  2 X+2  X  X  X X+2 X+2 X+2  2 X+2  2  X  X X+2  X  0
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  2  2  0  0  0  0  2  0  0  0  2  0  2  2  0  0  0  2  0  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  0  2  2  2  0  2  2  0  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  2
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  2  2  0  0  2  0  0  2  2  2  2  2  0  0  0  2  2  2  0  0  0  0  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  2  0  2  2  2  0  0  0  0  2  0  0  2  0  2  2  2  0  2  0  0  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+47x^34+94x^35+115x^36+236x^37+249x^38+296x^39+395x^40+394x^41+482x^42+434x^43+391x^44+298x^45+190x^46+174x^47+95x^48+94x^49+47x^50+24x^51+21x^52+2x^53+9x^54+2x^55+5x^56+1x^60

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 0.731 seconds.