The generator matrix

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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+240x^168+888x^169+732x^170+600x^171+1965x^172+2232x^173+1776x^174+1260x^175+2946x^176+3228x^177+2064x^178+1524x^179+4167x^180+4080x^181+2784x^182+2076x^183+4461x^184+4536x^185+3060x^186+2004x^187+3711x^188+3756x^189+2256x^190+1416x^191+2583x^192+2160x^193+936x^194+336x^195+837x^196+540x^197+192x^198+81x^200+84x^201+24x^202

The gray image is a linear code over GF(4) with n=244, k=8 and d=168.
This code was found by Heurico 1.16 in 16.6 seconds.