The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1 a^2*X  X  1  1  1  1 a^2*X
 0  1  1  a a^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  a  1 a*X+1 a^2*X+a a^2  1  X  X X+1 a^2*X+a a^2  1
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*X a^2*X a*X  X  0  X  X a^2*X  X  0 a*X a*X

generates a code of length 21 over F4[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+600x^60+63x^64+360x^68

The gray image is a linear code over GF(4) with n=84, k=5 and d=60.
This code was found by Heurico 1.16 in 0.593 seconds.