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

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+282x^66+32x^67+230x^68+224x^69+538x^70+224x^71+206x^72+32x^73+254x^74+9x^76+14x^78+1x^80+1x^124

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 10.9 seconds.