The generator matrix

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

generates a code of length 62 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+456x^171+750x^172+588x^173+888x^174+1812x^175+2370x^176+1332x^177+1548x^178+2688x^179+3651x^180+1788x^181+2256x^182+3636x^183+4371x^184+2076x^185+2652x^186+4284x^187+4578x^188+2088x^189+2556x^190+3912x^191+3918x^192+1920x^193+1752x^194+2292x^195+2127x^196+864x^197+588x^198+768x^199+657x^200+96x^201+48x^202+120x^203+102x^204+3x^208

The gray image is a linear code over GF(4) with n=248, k=8 and d=171.
This code was found by Heurico 1.16 in 18.7 seconds.