The generator matrix

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

generates a code of length 29 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+48x^77+396x^78+876x^79+276x^80+420x^81+1092x^82+1584x^83+399x^84+612x^85+1404x^86+1800x^87+696x^88+780x^89+1740x^90+1968x^91+378x^92+444x^93+744x^94+684x^95+15x^96+3x^100+12x^104+12x^108

The gray image is a linear code over GF(4) with n=116, k=7 and d=77.
This code was found by Heurico 1.16 in 41.2 seconds.