The generator matrix

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

generates a code of length 60 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+432x^165+720x^166+660x^167+819x^168+1464x^169+2256x^170+1464x^171+1569x^172+2676x^173+3780x^174+1956x^175+2139x^176+3612x^177+4404x^178+2484x^179+2529x^180+3696x^181+4980x^182+2796x^183+2499x^184+3456x^185+4200x^186+1776x^187+1455x^188+2340x^189+2268x^190+1020x^191+711x^192+684x^193+372x^194+132x^195+39x^196+72x^197+60x^198+12x^200+3x^208

The gray image is a linear code over GF(4) with n=240, k=8 and d=165.
This code was found by Heurico 1.16 in 17.8 seconds.