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

generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+72x^65+611x^66+1006x^67+1919x^68+1918x^69+2064x^70+2056x^71+2060x^72+1380x^73+1303x^74+746x^75+639x^76+266x^77+181x^78+76x^79+45x^80+26x^81+6x^82+4x^83+3x^86+2x^89

The gray image is a code over GF(2) with n=568, k=14 and d=260.
This code was found by Heurico 1.16 in 3.11 seconds.