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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 176.

Homogenous weight enumerator: w(x)=1x^0+405x^176+444x^177+288x^178+612x^180+492x^181+252x^182+312x^184+264x^185+72x^186+129x^188+144x^189+96x^190+180x^192+108x^193+24x^194+96x^196+84x^197+36x^198+48x^200+3x^204+6x^208

The gray image is a linear code over GF(4) with n=244, k=6 and d=176.
This code was found by Heurico 1.16 in 0.141 seconds.