The generator matrix

 1  0  1  1  1 X+2  1  1 3X+2  1  1 3X+2 X+2 2X+2  1  1  1  1 3X  1  1  2  1  1  1  1 3X 2X  1  1  1  1  1 3X  1 2X+2  0  0 2X+2 3X  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 3X+2  1  1 2X 3X+2 2X 2X+2 X+2  0  1  1  1
 0  1  1 2X+2 X+1  1  X 2X+1  1 3X+2 3X+1  1  1  1 2X+2 2X+3  X 3X+1  1 2X X+3  1 X+2 2X+1 3X+2  1  1  1  2 2X+3 X+3 X+1 X+2  1 2X+2  1  1  1  1  1  0  X  0  1 3X  3 X+3  3 X+3 3X+2 3X+3  3  0 3X+3  3 2X+1  3 X+2  1 X+1 X+3  1  1  1  1  1  1 X+2 2X  0
 0  0  X 3X 2X 3X 3X 2X  0  0  X 3X+2  2 2X+2 X+2  2 X+2 2X+2  X 2X+2 3X+2 X+2 2X+2 3X+2 3X+2 2X+2  0 3X  0 2X  X X+2 3X 2X+2  2 3X X+2  2 2X 3X+2 3X+2 2X+2 3X X+2  2  X  2 X+2 2X 2X  0  0 2X 2X+2 2X+2 X+2 3X  X 2X+2 3X+2 3X  X 2X 2X 3X+2  X 2X+2 X+2 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+14x^66+480x^67+214x^68+300x^69+68x^70+284x^71+190x^72+460x^73+14x^74+4x^75+8x^76+8x^77+2x^92+1x^96

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 0.265 seconds.