The generator matrix

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

generates a code of length 66 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+123x^184+186x^188+48x^189+216x^192+432x^193+75x^196+1296x^197+132x^200+1296x^201+42x^204+78x^208+39x^212+42x^216+21x^220+30x^224+15x^228+15x^232+3x^240+3x^244+3x^252

The gray image is a linear code over GF(4) with n=264, k=6 and d=184.
This code was found by Heurico 1.16 in 0.227 seconds.