The generator matrix

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

generates a code of length 67 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+117x^62+416x^63+1174x^64+1036x^65+1356x^66+962x^67+1048x^68+500x^69+539x^70+344x^71+347x^72+148x^73+138x^74+18x^75+12x^76+28x^77+2x^78+4x^79+1x^80+1x^88

The gray image is a code over GF(2) with n=536, k=13 and d=248.
This code was found by Heurico 1.16 in 0.782 seconds.