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 (a+1)X 0 1 1 (a+1)X 1 1 X 1 1 1 1 X 1 0 1 1 1 1 (a+1)X 1 1 1 aX 1 aX 1 1 1 1 1 1 X 1 1 1 1 1 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 0 1 X X+a (a+1)X+a 1 1 (a+1)X+a+1 a+1 1 a a 1 X+1 1 (a+1)X (a+1)X+a+1 X (a+1)X+1 X aX+a+1 X+1 (a+1)X+a+1 (a+1)X+a+1 0 X+a+1 a 1 1 X+1 1 X X+1 (a+1)X+a+1 X+a a+1 X+a 1 X+a (a+1)X+a aX (a+1)X aX+a 0 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 0 (a+1)X+a a+1 aX+a+1 aX+a+1 aX+a+1 X (a+1)X a+1 a+1 X (a+1)X+a aX+1 (a+1)X+1 (a+1)X+a+1 X X+a 1 (a+1)X 1 a+1 aX+a+1 0 aX+1 1 (a+1)X+1 X+1 aX X+a+1 0 a+1 1 a+1 a aX X+a+1 X+1 a+1 aX+a aX+a+1 a 0 aX 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 a+1 X+1 X aX+a+1 (a+1)X+1 X+a X+1 (a+1)X+a aX aX X+a+1 X+a a aX+1 X+a+1 aX+1 (a+1)X X+a aX (a+1)X+1 a aX+a (a+1)X (a+1)X+1 X+a+1 (a+1)X+a a+1 (a+1)X+a+1 1 aX+1 X+a+1 (a+1)X (a+1)X+1 aX+a aX X+1 a+1 aX+a+1 X+a+1 aX a+1 0 a aX+a 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 (a+1)X aX X X 0 (a+1)X X 0 0 X (a+1)X X aX (a+1)X 0 0 X aX aX (a+1)X X 0 aX aX 0 aX (a+1)X aX X 0 0 (a+1)X (a+1)X 0 X 0 aX aX X aX (a+1)X aX aX 0 generates a code of length 66 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 178. Homogenous weight enumerator: w(x)=1x^0+288x^178+360x^179+675x^180+756x^181+2088x^182+3312x^183+2292x^184+1776x^185+4416x^186+6468x^187+5505x^188+3756x^189+8616x^190+11040x^191+8142x^192+5868x^193+13968x^194+14976x^195+11439x^196+7368x^197+17280x^198+18720x^199+13563x^200+8052x^201+17580x^202+16836x^203+10587x^204+5772x^205+10968x^206+10272x^207+5442x^208+2772x^209+3960x^210+3504x^211+1509x^212+684x^213+696x^214+528x^215+162x^216+60x^217+12x^218+27x^220+15x^224+9x^228+15x^232+9x^236 The gray image is a linear code over GF(4) with n=264, k=9 and d=178. This code was found by Heurico 1.16 in 265 seconds.