The generator matrix

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

generates a code of length 66 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+1359x^192+1152x^196+600x^200+420x^204+360x^208+108x^212+84x^216+12x^224

The gray image is a linear code over GF(4) with n=264, k=6 and d=192.
This code was found by Heurico 1.16 in 118 seconds.