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.