The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+198x^60+1064x^61+2598x^62+3898x^63+5687x^64+7160x^65+8097x^66+8426x^67+8411x^68+7104x^69+5486x^70+3462x^71+2127x^72+1012x^73+441x^74+222x^75+79x^76+26x^77+26x^78+8x^79+1x^80+2x^85

The gray image is a code over GF(2) with n=536, k=16 and d=240.
This code was found by Heurico 1.16 in 35.2 seconds.