The generator matrix

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

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+65x^64+746x^65+790x^66+1262x^67+1059x^68+1118x^69+784x^70+872x^71+467x^72+434x^73+216x^74+218x^75+62x^76+70x^77+8x^78+16x^79+1x^80+2x^82+1x^84

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 0.844 seconds.