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

generates a code of length 63 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 182.

Homogenous weight enumerator: w(x)=1x^0+756x^182+414x^184+924x^186+252x^188+504x^190+153x^192+408x^194+96x^196+228x^198+66x^200+204x^202+36x^204+48x^206+6x^208

The gray image is a linear code over GF(4) with n=252, k=6 and d=182.
This code was found by Heurico 1.16 in 7.62 seconds.