The generator matrix 1 0 0 0 1 1 1 1 1 X 1 1 1 1 1 1 (a+1)X 1 1 aX 1 1 1 aX 1 1 1 1 1 1 (a+1)X 1 aX 1 1 (a+1)X 1 1 (a+1)X aX 1 X 1 1 1 1 1 1 1 1 1 (a+1)X X 1 1 1 0 1 1 1 1 (a+1)X aX 1 0 1 0 0 0 X X (a+1)X+1 aX+1 1 aX+a a+1 X+a (a+1)X+a+1 1 X (a+1)X a a 1 a+1 X+a aX+1 1 (a+1)X+1 X+a aX+a+1 X+a 1 0 0 (a+1)X+a+1 1 aX+a+1 X+a 1 aX aX+1 1 1 (a+1)X 1 (a+1)X+1 aX+1 aX+a+1 X+1 aX+a+1 a (a+1)X X+a+1 aX+a 1 1 (a+1)X (a+1)X+a+1 a 1 0 aX+1 aX X 1 1 aX 0 0 1 0 1 (a+1)X+a (a+1)X+a+1 X aX+a aX+a aX 0 aX+a+1 aX+1 a+1 X+a 1 aX+1 (a+1)X+a X+a X X (a+1)X+a+1 X aX+1 aX+a+1 1 aX 1 (a+1)X 1 a X+1 (a+1)X (a+1)X+a+1 a+1 1 X+a (a+1)X a aX+a (a+1)X+a+1 X+a+1 X+a+1 (a+1)X (a+1)X+a (a+1)X+1 aX+a (a+1)X+a+1 a (a+1)X+1 (a+1)X+a X+1 X X+1 0 (a+1)X+a aX+a X+1 aX+a+1 X+a+1 a+1 (a+1)X+a+1 X 0 0 0 1 a+1 a 1 (a+1)X+a aX (a+1)X+a (a+1)X+1 X+a+1 a aX+a 0 aX 1 aX+1 aX+1 (a+1)X X+1 (a+1)X+a X+a a+1 0 aX+a+1 (a+1)X+1 aX+a+1 X+a (a+1)X+1 X+a+1 a+1 (a+1)X+1 X aX+1 a+1 X+a a+1 (a+1)X+1 X+a+1 aX+1 (a+1)X+a aX+a+1 (a+1)X+1 a X+a X+a+1 (a+1)X+a+1 aX X aX aX+1 0 X+a X+a+1 aX X+1 aX+a aX+a+1 X+a X (a+1)X+1 X aX+1 0 0 0 0 X 0 aX 0 0 0 aX X aX X aX X aX X (a+1)X aX (a+1)X X 0 (a+1)X (a+1)X X aX (a+1)X X (a+1)X 0 0 (a+1)X X 0 X (a+1)X (a+1)X X 0 aX X 0 X (a+1)X (a+1)X aX 0 X 0 0 (a+1)X X aX 0 (a+1)X 0 (a+1)X X 0 (a+1)X aX X (a+1)X generates a code of length 64 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 172. Homogenous weight enumerator: w(x)=1x^0+264x^172+432x^173+480x^174+1056x^175+1878x^176+2004x^177+1644x^178+3996x^179+4800x^180+5460x^181+2952x^182+7152x^183+8412x^184+9276x^185+5244x^186+11304x^187+13215x^188+14064x^189+7056x^190+15576x^191+16824x^192+16656x^193+8256x^194+16356x^195+16893x^196+14340x^197+6888x^198+12096x^199+11256x^200+8412x^201+3180x^202+5088x^203+3474x^204+2760x^205+960x^206+1080x^207+684x^208+324x^209+204x^210+24x^211+60x^212+27x^216+18x^220+3x^224+9x^228+3x^232+3x^236 The gray image is a linear code over GF(4) with n=256, k=9 and d=172. This code was found by Heurico 1.16 in 255 seconds.