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

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

Homogenous weight enumerator: w(x)=1x^0+81x^66+120x^67+102x^68+880x^69+54x^70+536x^71+25x^72+32x^73+56x^74+96x^75+64x^76+1x^138

The gray image is a code over GF(2) with n=560, k=11 and d=264.
This code was found by Heurico 1.16 in 1.06 seconds.