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

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+153x^184+204x^185+432x^186+384x^187+477x^188+240x^189+240x^190+132x^191+348x^192+96x^193+204x^194+48x^195+168x^196+96x^197+108x^198+120x^199+141x^200+60x^201+96x^202+48x^203+99x^204+48x^205+60x^206+36x^207+21x^208+24x^209+12x^210

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 0.0818 seconds.