The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+20x^69+66x^70+86x^71+55x^72+18x^73+5x^74+2x^75+2x^85+1x^106

The gray image is a code over GF(2) with n=568, k=8 and d=276.
This code was found by Heurico 1.16 in 0.25 seconds.