The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+305x^66+536x^67+708x^68+448x^69+499x^70+440x^71+422x^72+200x^73+247x^74+80x^75+80x^76+88x^77+29x^78+3x^80+8x^82+2x^88

The gray image is a code over GF(2) with n=560, k=12 and d=264.
This code was found by Heurico 1.16 in 0.593 seconds.