The generator matrix

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

generates a code of length 61 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+180x^60+12x^62+48x^64+12x^66+2x^68+1x^72

The gray image is a code over GF(2) with n=488, k=8 and d=240.
This code was found by Heurico 1.16 in 3.47 seconds.