The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  2  0  0  1  1  1  1  1  1  1 X+2  X  1  1  1  1  0  1  1  1  1 X+2  2 X+2  1  0  0
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1  1  1  X  1 X+2  1  X  1  3  0 X+1  0  1  1  1 X+2 X+2 X+1 X+3  2  3  0  2  X  2  1  1  3  0  0
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  X X+1  1  X  1 X+1  X  X  0 X+1 X+3  0  3  2 X+1  0 X+1  2  1  1  2  0  1  1  1  3 X+1 X+3  1  1
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  0  0  0  0  2  2  2  0  0  2  2  2  0  0  2  0  0  0  0  2  0  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  0  2  0  2  2  0  2  2  2  0  0  0  0  2  2  2  0  0  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  2  0  2  2  0  0  0  2  0  0  2  0  2  0  0  2  0  2  2  2  2  0  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  2  0  2  2  2  2  0  2  2  2  0  2  0  2  2  0  0
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  2  2  2  0  2  0  0  0  0  0  2  0  0  2  2  0  2  0  2  0  2  2  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+134x^34+68x^35+666x^36+348x^37+1362x^38+596x^39+2497x^40+1036x^41+3084x^42+1036x^43+2388x^44+596x^45+1386x^46+348x^47+549x^48+68x^49+164x^50+40x^52+12x^54+1x^56+2x^58+2x^60

The gray image is a code over GF(2) with n=168, k=14 and d=68.
This code was found by Heurico 1.16 in 6.63 seconds.