The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 0 X X X aX 0 X X aX 0 (a+1)X (a+1)X X (a+1)X 0 0 (a+1)X (a+1)X X (a+1)X X 0 (a+1)X X
0 0 X 0 0 X (a+1)X aX aX aX 0 (a+1)X 0 aX aX 0 X X aX X X X aX X X 0 aX 0 0
0 0 0 X 0 (a+1)X 0 X aX (a+1)X X aX X 0 aX (a+1)X 0 X X X 0 aX aX X 0 aX X X 0
0 0 0 0 X X X (a+1)X X X X 0 0 0 (a+1)X (a+1)X X X (a+1)X (a+1)X X aX 0 (a+1)X aX (a+1)X 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 76.
Homogenous weight enumerator: w(x)=1x^0+225x^76+126x^80+183x^84+3072x^87+48x^88+234x^92+57x^96+102x^100+24x^104+21x^108+3x^116
The gray image is a linear code over GF(4) with n=116, k=6 and d=76.
This code was found by Heurico 1.16 in 9.35 seconds.