The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+104x^65+575x^66+908x^67+1382x^68+984x^69+1203x^70+704x^71+791x^72+446x^73+441x^74+254x^75+236x^76+90x^77+35x^78+22x^79+6x^80+8x^81+2x^86

The gray image is a code over GF(2) with n=560, k=13 and d=260.
This code was found by Heurico 1.16 in 0.906 seconds.