The generator matrix

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

generates a code of length 61 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+72x^166+288x^167+219x^168+1152x^169+420x^170+1284x^171+312x^172+2820x^173+1320x^174+2244x^175+558x^176+4644x^177+1992x^178+3432x^179+714x^180+5868x^181+2820x^182+3624x^183+909x^184+7344x^185+2868x^186+3684x^187+705x^188+5484x^189+2064x^190+2628x^191+465x^192+2868x^193+672x^194+1008x^195+81x^196+516x^197+60x^198+240x^199+39x^200+24x^201+27x^204+21x^208+24x^212+3x^216+6x^220+9x^224+3x^228

The gray image is a linear code over GF(4) with n=244, k=8 and d=166.
This code was found by Heurico 1.16 in 17.3 seconds.