The generator matrix

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

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+66x^64+562x^65+1385x^66+1364x^67+2146x^68+1826x^69+2386x^70+1680x^71+1856x^72+1082x^73+1000x^74+474x^75+254x^76+118x^77+91x^78+44x^79+26x^80+12x^81+1x^82+6x^83+2x^84+1x^86+1x^88

The gray image is a code over GF(2) with n=560, k=14 and d=256.
This code was found by Heurico 1.16 in 3.17 seconds.