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  1  1  1  1  1  X  0  X  X  1  0  0  X  0  0  1  1  1  X  1
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  0  X X+2  2  X  X X+2  0  2 X+2  2 X+2  X  2 X+2  X  X  X  X  X  0  2  X  X  X  X  2  0 X+2
 0  0  X  0  0  0  X X+2  X  2  X X+2  0 X+2  0 X+2 X+2  2  0  X  2 X+2  X  0  X  X  X  X  0  X  0  2  X  2 X+2  0  X  0  2  X  0 X+2
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  X X+2  2  2  0  2  0  0  X X+2  0  2  0 X+2 X+2  0  X  2  X X+2  X  0  X  2  X  0  0  2  X
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2  2  0 X+2  2  X  X X+2  2  2  2 X+2  0  X  0  0  X X+2 X+2  0  0  X  X  X X+2  2  X  X  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  2  2  2  2  2  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2  2  0  0  2  2  0  2  2  0  0  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+206x^34+8x^35+438x^36+48x^37+733x^38+312x^39+1084x^40+672x^41+1293x^42+632x^43+1084x^44+304x^45+643x^46+72x^47+402x^48+188x^50+62x^52+7x^54+1x^58+1x^62+1x^64

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 41 seconds.