The generator matrix

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

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+240x^54+936x^56+720x^58+672x^60+144x^62+951x^64+432x^66

The gray image is a linear code over GF(4) with n=80, k=6 and d=54.
This code was found by Heurico 1.16 in 0.093 seconds.