The generator matrix

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

generates a code of length 20 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+552x^51+264x^52+2136x^55+852x^56+4104x^59+1704x^60+4680x^63+1191x^64+816x^67+48x^68+36x^72

The gray image is a linear code over GF(4) with n=80, k=7 and d=51.
This code was found by Heurico 1.16 in 0.207 seconds.