The generator matrix

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

generates a code of length 60 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 172.

Homogenous weight enumerator: w(x)=1x^0+492x^172+168x^173+396x^175+552x^176+192x^177+180x^179+633x^180+144x^181+378x^184+192x^185+351x^188+72x^189+180x^191+135x^192+12x^195+3x^196+6x^200+9x^204

The gray image is a linear code over GF(4) with n=240, k=6 and d=172.
This code was found by Heurico 1.16 in 0.182 seconds.