The generator matrix

 1  0  1  1  1  1  1  1  1  1  0  1  1  1 (a+1)X  X  1  1  1  1 (a+1)X
 0  1  1  a (a+1)X+a+1  0 (a+1)X+1  a  X (a+1)X+a+1  1 aX+1 X+a X+a+1  1  X  X X+1 X+a X+a+1  1
 0  0 (a+1)X  X aX  X  0 (a+1)X aX (a+1)X (a+1)X aX  0  X  X  X (a+1)X  X aX  0 aX

generates a code of length 21 over F4[X,sigma]/(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 0.563 seconds.