The generator matrix

 1  0  1  1  1 3X+2  1  1 2X+2  1  1 2X  1  1  X  1  1  2  1 X+2  1  1 3X  1  1  1  1  1  1  2  1  1  1 X+2  1  2  X  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1 2X  1 2X+2  1  1  1  1  1 X+2  X  1
 0  1 X+1 3X+2  3  1 2X X+3  1 2X+2 X+1  1  X 2X+1  1  2 3X+3  1 X+2  1 2X+3 3X  1 2X+1 X+3  3  1 3X+3 2X  1  3 X+1 X+2  1 2X+2  1  1  2 X+1 3X 2X+1 3X+2  3 2X+1 3X+3 3X+1 3X  2  2  0 3X  X 2X  X  X 2X  0 3X+1  1  1 X+2  1 X+2 2X 2X+1 2X X+2  1 2X+2 2X
 0  0  2  2 2X  2 2X+2 2X+2 2X 2X  0 2X+2  2 2X  2 2X+2  0 2X+2  0  0  2 2X 2X 2X  2  0 2X+2  0 2X+2 2X+2  2 2X+2 2X 2X  0  0  2 2X+2  0  0  2  2 2X 2X+2  2 2X 2X+2  0  0 2X 2X+2  2 2X 2X  0  2  2 2X+2  0  2  0 2X  2  0  2 2X 2X+2 2X 2X+2 2X+2
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X 2X 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+66x^66+334x^67+234x^68+352x^69+166x^70+354x^71+133x^72+268x^73+76x^74+30x^75+24x^76+4x^77+2x^79+2x^86+1x^90+1x^106

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 0.375 seconds.