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  X  0  2  2  1  0  X  1  X  1  0  X  1  X  0  2  1  X  1
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2  0 X+2 X+2  0  0 X+2  2  0  2  X  2  X  0  0 X+2  2  X  2  X  X  0  0  2  0  0
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  0  2  2  0 X+2 X+2 X+2  2  X  X  2  0  2  X  2  X X+2 X+2  2  2  2  0 X+2 X+2  0
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0  2 X+2 X+2 X+2  2  X X+2  X  X  0  2  0  X  X  0  X  2  2  0  2  X  X  2  2  0
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  0  0  0  2  2  2  0  0  2  2  0  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  0  0  2  0  0  2  0  2  2  0  0  2  0  2  0  2  2  2  0  0  0  0  2
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  2  0  2  2  0  2  0  2  0  2  0  2  2  2  0  0  2  2  0  0  0  2  0  0  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+33x^34+70x^35+158x^36+196x^37+264x^38+294x^39+378x^40+498x^41+411x^42+476x^43+381x^44+254x^45+244x^46+160x^47+85x^48+62x^49+67x^50+22x^51+20x^52+14x^53+4x^54+2x^55+1x^58+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 0.694 seconds.