The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+101x^64+500x^65+1377x^66+2190x^67+3005x^68+3464x^69+3923x^70+4270x^71+3795x^72+3518x^73+2591x^74+1762x^75+1202x^76+500x^77+277x^78+138x^79+82x^80+22x^81+24x^82+8x^83+5x^84+8x^85+1x^88+4x^89

The gray image is a code over GF(2) with n=568, k=15 and d=256.
This code was found by Heurico 1.16 in 11.7 seconds.