The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1  X  1 X+2  2  1  0  1  X  1  1  1  1  2 X+2  X  1  1  1  1  0  1  X  1  0  1  1  X  2  X  0  1  1  2  1  X X+2  1  0  1  0 X+2  1  1  2  1  1  1 X+2  1  2  1  0  1  X  0  1
 0  1  0  0  1 X+1  1  0 X+2  2  3  1  1  1  2  0  1 X+3  1 X+1  2 X+2  3  1 X+2  1 X+1  X X+2  1  1 X+1  1 X+3  1  X  1  1  1  1  X  3  X  1 X+2  1  0  2  X X+1  2  1 X+1  2  1 X+3 X+1  2 X+2 X+3  1  3  0  2  2  1  1
 0  0  1  1  1  2  3  1  3  X X+2 X+3 X+1  X  1 X+1 X+2  0 X+1  3 X+2 X+3  3  2  1  3  X  0 X+2  2 X+3 X+3  2  1  1 X+1  0  2  3  2  1  0  1  1  3 X+2  1 X+2  1  X  1  1 X+3 X+2 X+3  3 X+3  1  1  2  0 X+3  1 X+1  1 X+3  3
 0  0  0  X X+2  0 X+2 X+2 X+2  0  0 X+2 X+2  0  X  2 X+2  X  2  0  X  0  2  X  0  2  X  2  X  2  X  2  0  X  X  X  0 X+2  0  X  X X+2 X+2  2  0  2  0  2  0  0 X+2 X+2 X+2 X+2 X+2  2 X+2  0  2  0  X  X  0  2  X  2 X+2
 0  0  0  0  2  0  2  2  2  2  2  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0  0  2  2  2  0  2  2  2  0  0  2  0  0  0  0  2  2  2  0  0  0  0  0  2  2  2  0  0  2  0  2  2  2  2  2  0

generates a code of length 67 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+206x^61+157x^62+616x^63+191x^64+606x^65+229x^66+520x^67+164x^68+436x^69+111x^70+314x^71+67x^72+202x^73+71x^74+104x^75+23x^76+50x^77+8x^78+10x^79+1x^80+4x^81+4x^83+1x^84

The gray image is a code over GF(2) with n=268, k=12 and d=122.
This code was found by Heurico 1.16 in 28.9 seconds.