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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+271x^64+144x^65+450x^66+284x^67+790x^68+464x^69+678x^70+256x^71+334x^72+88x^73+150x^74+36x^75+98x^76+8x^77+34x^78+9x^80+1x^112

The gray image is a code over GF(2) with n=552, k=12 and d=256.
This code was found by Heurico 1.16 in 0.625 seconds.