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

generates a code of length 67 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+110x^62+258x^64+192x^66+1024x^67+156x^68+204x^70+28x^72+48x^74+4x^76+22x^78+1x^128

The gray image is a code over GF(2) with n=536, k=11 and d=248.
This code was found by Heurico 1.16 in 26 seconds.