The generator matrix

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

generates a code of length 24 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+684x^63+333x^64+2400x^67+852x^68+3672x^71+1602x^72+4224x^75+1128x^76+1308x^79+138x^80+36x^84+6x^88

The gray image is a linear code over GF(4) with n=96, k=7 and d=63.
This code was found by Heurico 1.16 in 0.348 seconds.