The generator matrix

 1  0  1  1  1 3X+2  1  X  1 2X  1  1  2  1  1  1 X+2  1  1 2X+2  1 3X  1  1  1  1  1 3X  1  0  1  1  1  1  1 2X 3X+2  1  1  1  1  1 2X  X  2  1  1 X+2  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1 3X+2 2X  1  1
 0  1 X+1 X+2 2X+3  1 2X+2  1 X+3  1 3X  1  1 2X X+1 3X+2  1 3X+3  2  1  X  1 X+1 3X+3  3 2X+1  0  1  3  1 3X+2 3X+1  2 2X+3 X+2  1  1 2X+1 2X+2 3X X+2 3X+1  1  1  1 2X  1  1  0  X  2 3X 2X  2 3X  X 2X+2  2 2X X+2 X+2 3X+2 2X  X  1 3X+1  1  X 3X+2 2X+3
 0  0  2  0 2X+2  2  0  2 2X+2 2X+2  0  2 2X+2  2 2X 2X+2  0 2X  2  0 2X+2  0 2X 2X  0 2X  0  0 2X  0 2X+2  2  2 2X+2 2X  2  2  0  0 2X  2  2 2X  2  2 2X+2 2X+2 2X 2X+2 2X+2 2X  2  2  0  0  0 2X 2X  0  2 2X 2X  2  2  0 2X+2 2X  2  0 2X+2
 0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X  0 2X  0 2X  0  0  0 2X  0 2X  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X
 0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0 2X  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0  0  0 2X  0  0  0 2X 2X  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+114x^65+279x^66+494x^67+345x^68+708x^69+335x^70+660x^71+321x^72+462x^73+205x^74+94x^75+33x^76+20x^77+5x^78+2x^80+4x^81+6x^82+2x^84+4x^85+2x^98

The gray image is a code over GF(2) with n=560, k=12 and d=260.
This code was found by Heurico 1.16 in 0.531 seconds.