The generator matrix
1 0 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 X 1 1 1 1 1 1 1 aX X X 1 1
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 (a+1)X+a+1 aX+a+1 X 1 (a+1)X+1 X+a+1 aX X+1 aX+a 1 (a+1)X+a 1 0 X X+a X+1
0 0 (a+1)X 0 X X (a+1)X X (a+1)X X 0 0 X X 0 (a+1)X (a+1)X aX 0 aX aX X X 0 (a+1)X (a+1)X (a+1)X 0 aX aX
0 0 0 X aX X aX (a+1)X (a+1)X 0 X (a+1)X 0 aX aX 0 aX X (a+1)X aX (a+1)X aX 0 0 (a+1)X X aX (a+1)X X (a+1)X
generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 81.
Homogenous weight enumerator: w(x)=1x^0+144x^81+96x^82+180x^83+87x^84+540x^85+204x^86+168x^87+78x^88+540x^89+156x^90+144x^91+36x^92+756x^93+228x^94+216x^95+21x^96+324x^97+84x^98+60x^99+6x^100+6x^104+12x^108+6x^112+3x^116
The gray image is a linear code over GF(4) with n=120, k=6 and d=81.
This code was found by Heurico 1.16 in 1.89 seconds.