The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+163x^62+1026x^63+2656x^64+4934x^65+7459x^66+10498x^67+13488x^68+16116x^69+17783x^70+16864x^71+14299x^72+10518x^73+6925x^74+4348x^75+2255x^76+946x^77+424x^78+246x^79+62x^80+28x^81+12x^82+10x^83+5x^84+2x^85+2x^86+2x^88

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 157 seconds.