The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  1  1  1  1  1  1  1  1  X  1  1 aX
 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  X X+a  X aX+a  X (a+1)X+a  a  0 aX+a+1 aX+a (a+1)X (a+1)X X+a+1 X+1  1
 0  0 (a+1)X  0  X  X (a+1)X  X (a+1)X  X  0  0  X  X aX  0  0 (a+1)X (a+1)X  X aX  X (a+1)X aX  0 (a+1)X aX  0 aX
 0  0  0  X aX  X aX (a+1)X (a+1)X  0  X (a+1)X  0 aX  X  0 aX  X aX aX  0 (a+1)X  0  X aX  0 (a+1)X (a+1)X (a+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+729x^80+948x^84+1272x^88+924x^92+207x^96+12x^104+3x^112

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 1.44 seconds.