The generator matrix

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

generates a code of length 60 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+408x^168+192x^169+468x^171+1719x^172+564x^173+624x^175+2322x^176+708x^177+660x^179+1989x^180+624x^181+564x^183+1683x^184+480x^185+528x^187+1218x^188+348x^189+204x^191+711x^192+156x^193+24x^195+180x^196+3x^200+3x^204+3x^212

The gray image is a linear code over GF(4) with n=240, k=7 and d=168.
This code was found by Heurico 1.16 in 0.85 seconds.