The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+110x^64+630x^65+864x^66+1242x^67+1063x^68+1128x^69+863x^70+780x^71+476x^72+430x^73+242x^74+230x^75+44x^76+32x^77+45x^78+4x^79+1x^80+4x^81+1x^82+1x^84+1x^90

The gray image is a code over GF(2) with n=552, k=13 and d=256.
This code was found by Heurico 1.16 in 0.891 seconds.