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

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

Homogenous weight enumerator: w(x)=1x^0+34x^70+2x^71+19x^72+4x^73+2x^74+2x^75

The gray image is a code over GF(2) with n=560, k=6 and d=280.
This code was found by Heurico 1.16 in 0.188 seconds.