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

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+142x^68+128x^69+480x^70+128x^71+142x^72+2x^76+1x^128

The gray image is a code over GF(2) with n=560, k=10 and d=272.
This code was found by Heurico 1.16 in 0.219 seconds.