The generator matrix

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

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+112x^64+582x^65+1160x^66+1702x^67+2026x^68+1972x^69+2044x^70+1938x^71+1595x^72+1266x^73+786x^74+510x^75+368x^76+170x^77+69x^78+38x^79+22x^80+8x^81+4x^82+4x^83+4x^84+2x^85+1x^86

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 3.34 seconds.