The generator matrix

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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+212x^62+1210x^63+2622x^64+4178x^65+5678x^66+6558x^67+8208x^68+8472x^69+8274x^70+6930x^71+5531x^72+3386x^73+2249x^74+1298x^75+412x^76+182x^77+74x^78+36x^79+8x^80+4x^81+7x^82+2x^84+2x^85+2x^86

The gray image is a code over GF(2) with n=552, k=16 and d=248.
This code was found by Heurico 1.16 in 38.7 seconds.