The generator matrix

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

generates a code of length 29 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+84x^68+12x^69+438x^72+72x^73+48x^75+1335x^76+324x^77+576x^79+3969x^80+1584x^81+2592x^83+9933x^84+3924x^85+5184x^87+14061x^88+4104x^89+3888x^91+9183x^92+2268x^93+1428x^96+363x^100+129x^104+30x^108+6x^112

The gray image is a linear code over GF(4) with n=116, k=8 and d=68.
This code was found by Heurico 1.16 in 7.77 seconds.