The generator matrix
1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 X 1 1 aX
0 1 1 a (a+1)X+a+1 0 (a+1)X+1 a (a+1)X+a+1 1 0 a (a+1)X+1 1 X X+a X aX+a X (a+1)X+a a 0 aX+a+1 aX+a (a+1)X (a+1)X X+a+1 X+1 1
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 X X aX 0 0 (a+1)X (a+1)X X aX X (a+1)X aX 0 (a+1)X aX 0 aX
0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X 0 aX X 0 aX X aX aX 0 (a+1)X 0 X aX 0 (a+1)X (a+1)X (a+1)X
generates a code of length 29 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+729x^80+948x^84+1272x^88+924x^92+207x^96+12x^104+3x^112
The gray image is a linear code over GF(4) with n=116, k=6 and d=80.
This code was found by Heurico 1.16 in 1.44 seconds.