The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  X (a+1)X (a+1)X  0  1  1 aX  1  1
 0  1  0 (a+1)X  X aX  1 (a+1)X+1  a aX+1 a+1 (a+1)X+a X+a X+a+1 aX+a+1 X+1 aX+a (a+1)X+a+1  1  1  1  1  1  1 aX (a+1)X  1 a+1 (a+1)X+a+1
 0  0  1  1 (a+1)X+a (a+1)X+a+1 a+1  a  X (a+1)X X+a+1 X+1 aX+a aX+1 aX (a+1)X+1 aX+a+1 X+a  1 (a+1)X aX  1 X+1 (a+1)X+a+1 aX+1 aX X+1 (a+1)X+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+201x^80+228x^81+240x^82+144x^83+732x^84+444x^85+264x^86+96x^87+300x^88+156x^89+96x^90+144x^91+414x^92+324x^93+168x^94+138x^96+6x^100

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 0.032 seconds.