The generator matrix

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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+294x^180+288x^182+258x^184+96x^186+18x^188+63x^192+6x^208

The gray image is a linear code over GF(4) with n=244, k=5 and d=180.
This code was found by Heurico 1.16 in 0.032 seconds.