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  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  X  1  1 X^2  1 X^2+2  1  1  2  1  1  1  1  X  1 X^2+2  1  2  2  1  1  2  2  X
 0  X  0  X  0  2 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2  0 X^2+2  X X^2+X+2  X X^2  X  2  2  2 X+2 X^2  0 X^2+X X^2+X+2 X^2 X^2+X+2 X+2 X^2+2 X+2  2  X X^2+X  0  0  0 X^2 X^2+X+2  X X^2+X X^2+X+2 X^2+X+2 X^2 X^2 X^2+2  X  X X^2+X+2 X^2  0  0  X X^2 X^2+X+2 X^2+2  0  X X^2+2  X X^2+X  2  X  X X^2+2
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2  X  0  2 X^2+X+2 X+2 X^2  0 X+2  X X^2 X^2+X+2 X^2 X^2  X X^2+X+2 X^2+2  0 X^2+X+2 X^2+X X+2  0  0 X+2  2  2 X^2+X X+2 X+2 X^2+X X^2 X^2+X+2 X^2+2 X^2+X X^2+X  0 X^2 X^2+2  X  2  X X^2+X+2 X^2+X+2  0  0  X  2  X X^2+2  X  X  X  X X^2+2  X X^2  2 X^2+X X^2+X+2 X^2 X+2
 0  0  0  2  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  2  2  0  2  2  2  0  2  0  0  0  2  2  0  0  0  0  0  2  0  2  0  2  2  2  0  0  2  0  0  0  0  2  2  2  2  0  0
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  0  0  0  0  2  2  0  2  0  2  2  0  2  0  0  2  0  0  0  0  2  0  2  0  0  2  2  2  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0

generates a code of length 70 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+214x^65+293x^66+324x^67+406x^68+634x^69+576x^70+530x^71+385x^72+262x^73+187x^74+124x^75+40x^76+38x^77+30x^78+42x^79+4x^81+1x^82+4x^83+1x^114

The gray image is a code over GF(2) with n=560, k=12 and d=260.
This code was found by Heurico 1.16 in 83.5 seconds.