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.