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

generates a code of length 70 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+30x^69+206x^70+14x^72+1x^78+1x^80+2x^85+1x^94

The gray image is a code over GF(2) with n=560, k=8 and d=276.
This code was found by Heurico 1.16 in 0.328 seconds.