The generator matrix

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

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+64x^62+276x^63+513x^64+530x^65+499x^66+480x^67+449x^68+512x^69+389x^70+196x^71+109x^72+44x^73+13x^74+8x^75+3x^76+2x^78+2x^81+2x^84+3x^88+1x^94

The gray image is a code over GF(2) with n=536, k=12 and d=248.
This code was found by Heurico 1.16 in 0.406 seconds.