The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+172x^63+1246x^64+2728x^65+3874x^66+5920x^67+6882x^68+8276x^69+8094x^70+8172x^71+6916x^72+5420x^73+3464x^74+2316x^75+1113x^76+556x^77+202x^78+88x^79+71x^80+12x^81+6x^82+4x^83+3x^84

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 39.1 seconds.