The generator matrix

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

generates a code of length 19 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+144x^53+360x^54+36x^56+96x^57+24x^60+144x^61+216x^62+3x^64

The gray image is a linear code over GF(4) with n=76, k=5 and d=53.
This code was found by Heurico 1.16 in -1.01e-007 seconds.