The generator matrix

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

generates a code of length 65 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+322x^62+332x^63+382x^64+254x^65+220x^66+208x^67+162x^68+38x^69+64x^70+32x^71+22x^72+9x^76+1x^78+1x^90

The gray image is a code over GF(2) with n=520, k=11 and d=248.
This code was found by Heurico 1.16 in 7.86 seconds.