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

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+280x^65+141x^66+486x^67+420x^68+574x^69+471x^70+544x^71+368x^72+384x^73+83x^74+190x^75+32x^76+70x^77+9x^78+28x^79+10x^80+4x^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 43.5 seconds.