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

generates a code of length 70 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+71x^64+4x^65+118x^66+48x^67+211x^68+328x^69+496x^70+336x^71+239x^72+52x^73+58x^74+44x^76+28x^78+9x^80+4x^82+1x^124

The gray image is a code over GF(2) with n=560, k=11 and d=256.
This code was found by Heurico 1.16 in 0.437 seconds.