The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+28x^70+186x^71+31x^72+4x^75+3x^78+2x^79+1x^86

The gray image is a code over GF(2) with n=568, k=8 and d=280.
This code was found by Heurico 1.16 in 0.125 seconds.