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 aX  0  1  1  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 aX+a X+a a+1 (a+1)X  1  1  1 X+1 (a+1)X+a+1 a+1 (a+1)X+a  0  X (a+1)X  1 aX+a+1 (a+1)X+a+1 aX+a X+a aX+a+1  1  a  X aX+1 X+1  1 aX  1 aX+a a+1 (a+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 (a+1)X X+a aX+1 aX  a (a+1)X+1  1 X+a aX+a+1  X aX+a (a+1)X+a+1 a+1 aX+a+1  0 X+a aX+a aX (a+1)X+a aX+a+1 X+1 a+1 aX+1 (a+1)X+a+1  a X+a+1  a  1  1 aX+a+1  X (a+1)X+a+1 (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+234x^172+192x^173+432x^174+288x^175+426x^176+240x^177+264x^178+204x^179+237x^180+120x^181+144x^182+132x^183+288x^184+72x^185+120x^186+108x^187+90x^188+96x^189+144x^190+12x^191+63x^192+24x^193+48x^194+24x^195+63x^196+24x^197+6x^200

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 0.078 seconds.