The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+166x^60+1184x^61+2580x^62+3800x^63+5582x^64+6996x^65+8479x^66+8468x^67+8473x^68+6844x^69+5604x^70+3524x^71+1919x^72+1082x^73+519x^74+160x^75+53x^76+52x^77+26x^78+16x^79+6x^80+2x^81

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 36.6 seconds.