The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+612x^64+1172x^65+2272x^66+2768x^67+3897x^68+3764x^69+4226x^70+3988x^71+3677x^72+2504x^73+1912x^74+912x^75+557x^76+204x^77+172x^78+44x^79+50x^80+4x^81+24x^82+6x^84+2x^86

The gray image is a code over GF(2) with n=560, k=15 and d=256.
This code was found by Heurico 1.16 in 26.8 seconds.