The generator matrix

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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+154x^62+120x^63+330x^64+216x^65+504x^66+212x^67+265x^68+64x^69+87x^70+16x^71+59x^72+8x^73+6x^74+4x^75+1x^78+1x^116

The gray image is a code over GF(2) with n=528, k=11 and d=248.
This code was found by Heurico 1.16 in 0.343 seconds.