The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X aX  1  1  1  1  1 (a+1)X  X  1  X
 0  1  0 (a+1)X  X aX  1 (a+1)X+1  a (a+1)X+a X+1 (a+1)X+a+1 aX+a aX+a+1 X+a+1 aX+1 X+a a+1  1  1  1 (a+1)X  X X+a  a  a  1 (a+1)X  X  1
 0  0  1  1 (a+1)X+a (a+1)X+a+1 a+1  a  X X+1 (a+1)X+1 X+a aX+a+1 aX aX+1 (a+1)X aX+a X+a+1  1 (a+1)X+a (a+1)X+a X+1 aX+1  X (a+1)X (a+1)X+1 aX+a  1  a (a+1)X+a+1

generates a code of length 30 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+216x^83+222x^84+216x^85+216x^86+660x^87+501x^88+144x^89+216x^90+336x^91+141x^92+72x^93+72x^94+372x^95+342x^96+144x^97+72x^98+144x^99+9x^100

The gray image is a linear code over GF(4) with n=120, k=6 and d=83.
This code was found by Heurico 1.16 in 0.031 seconds.