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.