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  X  X  X  X  X  X  X  1  1  1  1  1  1  X  X  X  X X^2 X^2 X^2 X^2 X^2 X^2 X^2  X  X  X  1  X  1  1  1  X  1  1  1  1  X  1
 0  2  0  0  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  0
 0  0  2  0  2  2  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  0  2  2  0  0
 0  0  0  2  2  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  2  0  2  0  2  0  0  2  2  0  0  0  2  2  0  0  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+34x^60+72x^61+4x^62+6x^63+1x^64+3x^66+4x^68+2x^71+1x^74

The gray image is a code over GF(2) with n=488, k=7 and d=240.
This code was found by Heurico 1.16 in 0.109 seconds.