The generator matrix

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

generates a code of length 24 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+321x^64+894x^68+1515x^72+1227x^76+111x^80+12x^84+9x^88+3x^92+3x^96

The gray image is a linear code over GF(4) with n=96, k=6 and d=64.
This code was found by Heurico 1.16 in 0.0293 seconds.