The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 1 1 1 X X 1 1 1 X X 1 X X^2 0 X X^2 2 X X 1 X^2 1 1 X X X X 1 X^2 X^2 X^2 X^2 0 2 2 0 1 1
0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 0 X^2+2 2 X^2 X^2+2 X^2 0 X^2+2 2 X^2 X^2+2 X^2 0 2 X^2+2 0 2 X^2 X^2+2 X^2+2 X^2 X^2 X^2 X^2 0 2 0 2 2 X^2+2 0 2 X^2+2 X^2 X^2 X^2+2 X^2 0 2 X^2 X^2 2 2 0 0
generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 61.
Homogenous weight enumerator: w(x)=1x^0+32x^61+22x^62+5x^64+2x^66+2x^68
The gray image is a code over GF(2) with n=488, k=6 and d=244.
This code was found by Heurico 1.16 in 0.141 seconds.