The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+655x^64+1100x^65+2234x^66+2696x^67+4016x^68+3744x^69+4630x^70+3752x^71+3517x^72+2416x^73+1964x^74+912x^75+679x^76+168x^77+150x^78+32x^79+51x^80+28x^81+14x^82+9x^84

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 13.7 seconds.