The generator matrix

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

generates a code of length 64 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+360x^184+168x^185+396x^187+912x^188+192x^189+180x^191+465x^192+144x^193+276x^196+192x^197+279x^200+72x^201+180x^203+243x^204+12x^207+12x^208+6x^212+3x^216+3x^220

The gray image is a linear code over GF(4) with n=256, k=6 and d=184.
This code was found by Heurico 1.16 in 0.117 seconds.