The generator matrix

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

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+264x^52+1536x^53+900x^56+3072x^57+1584x^60+4608x^61+1263x^64+3072x^65+72x^68+12x^72

The gray image is a linear code over GF(4) with n=80, k=7 and d=52.
This code was found by Heurico 1.16 in 5.95 seconds.