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

generates a code of length 66 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+35x^64+136x^65+699x^66+112x^67+28x^68+8x^69+4x^70+1x^130

The gray image is a code over GF(2) with n=528, k=10 and d=256.
This code was found by Heurico 1.16 in 20.4 seconds.