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 2X+2  1  1  1  1  1  1  X  1  1  1  1 2X  1  1  1  1  X  1  1
 0  2  0  2  0  2  0 2X+2 2X  2  2  0  2  0 2X 2X+2  0  2 2X 2X+2  0  2 2X 2X+2  0  2 2X 2X+2  2  0 2X 2X+2 2X+2 2X  0  2  2 2X+2  0 2X  2 2X 2X+2  0 2X+2  0 2X+2 2X 2X 2X 2X  2  2  2  0  0  2  0  0 2X  2  2 2X  0 2X  2 2X+2  0  0  0
 0  0 2X  0  0  0  0  0 2X  0  0  0  0 2X 2X  0  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X 2X  0  0 2X  0  0 2X  0  0  0 2X  0  0 2X  0  0  0 2X 2X  0  0  0
 0  0  0 2X  0  0  0 2X  0  0  0  0 2X  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X  0 2X 2X  0  0 2X  0  0
 0  0  0  0 2X  0  0  0  0  0  0 2X  0 2X 2X  0  0 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0 2X 2X  0  0 2X  0  0  0 2X 2X  0 2X 2X  0 2X  0  0  0
 0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X  0 2X  0  0  0  0 2X  0  0  0  0  0  0
 0  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0 2X 2X  0 2X 2X 2X 2X  0 2X 2X  0  0  0 2X  0  0  0 2X 2X 2X 2X  0  0  0 2X  0  0  0 2X  0  0 2X 2X  0  0  0  0 2X 2X  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+63x^64+120x^66+87x^68+512x^69+576x^70+512x^71+56x^72+48x^74+24x^76+8x^80+24x^82+16x^84+1x^132

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 0.468 seconds.