The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+174x^62+984x^63+2818x^64+4594x^65+7634x^66+9950x^67+15056x^68+15108x^69+18262x^70+15446x^71+15418x^72+10202x^73+7420x^74+3924x^75+2318x^76+1034x^77+404x^78+152x^79+95x^80+36x^81+22x^82+6x^83+6x^84+2x^85+4x^86+2x^87

The gray image is a code over GF(2) with n=560, k=17 and d=248.
This code was found by Heurico 1.16 in 158 seconds.