The generator matrix

 1  0  1  1  1 X+2  1  1 3X  1  1 2X+2  1  1 2X+2  1  1 3X  1  1 X+2  1  1  0  1  1 2X  1  1 3X+2  1  1  1  1  2  X  1  1  1  1  1  1  1  1 2X 3X+2  2  X  X  X  0  X  X 2X+2  X  X  0  X  X 2X+2  X  X  X  X  1 2X+2  1 2X+2  2  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  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 X+3  1  1  1 2X 3X+2  2  X 3X+1 2X+3 X+3  1  1  1  1  1  0 X+2  X 2X+2 3X  X  0 X+2  X 2X+2 3X  X 2X  2  2 2X 3X+3  1 3X+3  1  0  0
 0  0 2X 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0  0 2X 2X  0 2X  0 2X  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X  0 2X  0  0  0 2X 2X  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+94x^68+64x^69+176x^70+112x^71+33x^72+8x^73+16x^74+4x^75+4x^79

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 0.203 seconds.