The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+292x^65+143x^66+420x^67+373x^68+644x^69+545x^70+616x^71+333x^72+292x^73+97x^74+156x^75+27x^76+100x^77+15x^78+24x^79+1x^80+16x^81+1x^112

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 8.25 seconds.