The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+216x^63+1406x^64+2478x^65+4202x^66+5326x^67+6879x^68+8144x^69+8695x^70+8048x^71+7075x^72+5298x^73+3803x^74+1850x^75+1121x^76+504x^77+301x^78+108x^79+38x^80+20x^81+7x^82+4x^83+8x^84+4x^85

The gray image is a code over GF(2) with n=560, k=16 and d=252.
This code was found by Heurico 1.16 in 39.5 seconds.