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

generates a code of length 70 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+38x^68+432x^70+38x^72+1x^76+1x^100+1x^104

The gray image is a code over GF(2) with n=560, k=9 and d=272.
This code was found by Heurico 1.16 in 0.312 seconds.