The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+97x^60+792x^61+2177x^62+4860x^63+8765x^64+14364x^65+21119x^66+26938x^67+33961x^68+35284x^69+34143x^70+28668x^71+20976x^72+14046x^73+8408x^74+4014x^75+2022x^76+858x^77+344x^78+172x^79+64x^80+46x^81+15x^82+4x^83+2x^84+2x^85+2x^86

The gray image is a code over GF(2) with n=552, k=18 and d=240.
This code was found by Heurico 1.16 in 607 seconds.