The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1
0 X 0 0 0 0 X X X aX 0 X (a+1)X aX aX (a+1)X X X X 0 aX X aX aX (a+1)X X aX aX 0 aX
0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX aX 0 0 aX (a+1)X X 0 aX X (a+1)X 0 X X (a+1)X X X
0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X (a+1)X 0 X 0 X 0 aX (a+1)X (a+1)X aX (a+1)X (a+1)X 0 X X X 0
0 0 0 0 X X X (a+1)X X X X aX 0 aX 0 0 aX aX aX aX X (a+1)X 0 (a+1)X aX 0 X 0 (a+1)X X
generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 80.
Homogenous weight enumerator: w(x)=1x^0+348x^80+192x^84+1392x^88+1728x^92+285x^96+120x^104+30x^112
The gray image is a linear code over GF(4) with n=120, k=6 and d=80.
This code was found by Heurico 1.16 in 89.7 seconds.