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

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+151x^66+148x^67+261x^68+268x^69+502x^70+244x^71+232x^72+52x^73+63x^74+40x^75+64x^76+16x^77+4x^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 0.406 seconds.