The generator matrix

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

generates a code of length 24 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+147x^68+192x^69+144x^70+159x^72+96x^73+129x^76+96x^77+48x^78+9x^80+3x^96

The gray image is a linear code over GF(4) with n=96, k=5 and d=68.
This code was found by Heurico 1.16 in -3.62e-008 seconds.