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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+154x^64+48x^66+192x^67+328x^68+640x^69+288x^70+192x^71+96x^72+48x^74+56x^76+4x^80+1x^128

The gray image is a code over GF(2) with n=552, k=11 and d=256.
This code was found by Heurico 1.16 in 0.719 seconds.