The generator matrix

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

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+411x^176+504x^177+396x^178+525x^180+456x^181+180x^182+303x^184+144x^185+249x^188+192x^189+246x^192+216x^193+180x^194+39x^196+24x^197+12x^198+9x^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 50.5 seconds.