The generator matrix
1 0 1 1 1 1 1 1 1 1 0 1 1 1 X 1 1 1 1 1 1 1 1 1 1 X 1 1
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a X (a+1)X+a+1 1 (a+1)X+1 X+a aX+a+1 1 X (a+1)X (a+1)X aX+1 aX+1 1 X+a (a+1)X+a (a+1)X+a aX+a+1 1 a+1 a+1
0 0 (a+1)X X aX X 0 (a+1)X aX (a+1)X (a+1)X X aX 0 aX X aX 0 (a+1)X 0 X (a+1)X aX X (a+1)X (a+1)X aX 0
generates a code of length 28 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+81x^80+576x^82+96x^84+72x^88+192x^90+3x^96+3x^112
The gray image is a linear code over GF(4) with n=112, k=5 and d=80.
This code was found by Heurico 1.16 in 0.016 seconds.