The generator matrix

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

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+60x^65+724x^66+792x^67+1381x^68+1020x^69+1165x^70+648x^71+855x^72+420x^73+503x^74+252x^75+206x^76+60x^77+86x^78+12x^79+4x^80+1x^82+1x^84+1x^86

The gray image is a code over GF(2) with n=560, k=13 and d=260.
This code was found by Heurico 1.16 in 0.828 seconds.