The generator matrix

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

generates a code of length 24 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+360x^66+228x^67+228x^68+480x^69+768x^70+228x^71+174x^72+264x^74+204x^75+228x^76+288x^77+528x^78+108x^79+9x^80

The gray image is a linear code over GF(4) with n=96, k=6 and d=66.
This code was found by Heurico 1.16 in 0.016 seconds.