The generator matrix

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

generates a code of length 66 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+52x^61+642x^62+818x^63+1402x^64+988x^65+1161x^66+840x^67+750x^68+528x^69+456x^70+182x^71+262x^72+32x^73+45x^74+16x^75+16x^76+1x^88

The gray image is a code over GF(2) with n=528, k=13 and d=244.
This code was found by Heurico 1.16 in 0.765 seconds.