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

generates a code of length 29 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+21x^84+192x^87+36x^88+3x^96+3x^116

The gray image is a linear code over GF(4) with n=116, k=4 and d=84.
This code was found by Heurico 1.16 in -3.24e-008 seconds.