The generator matrix

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

generates a code of length 21 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+312x^57+576x^59+600x^60+504x^61+384x^63+63x^64+360x^65+576x^67+360x^68+360x^69

The gray image is a linear code over GF(4) with n=84, k=6 and d=57.
This code was found by Heurico 1.16 in 1.33 seconds.