The generator matrix 1 0 0 0 1 1 1 1 1 X 1 1 1 1 1 0 X 1 1 1 1 1 1 a*X 1 0 1 1 a^2*X 1 1 1 1 1 a*X 1 a*X 1 1 1 1 0 1 1 1 1 1 1 a^2*X 1 1 1 1 1 1 1 1 1 1 a*X 1 1 1 a^2*X X a*X 0 1 0 0 0 X X a^2*X+1 a*X+1 1 a^2*X+a a*X+a a*X+a^2 a^2 a^2*X+1 1 1 a*X a*X a*X+1 a^2 a^2*X+1 a^2*X+a^2 X a^2*X+1 1 X+a a*X+a^2 1 X+a 0 a*X+1 a^2*X+a X 1 1 1 1 a^2*X+a 1 X+a 1 a^2*X+a a^2*X+a^2 a*X+a^2 X+a 1 0 1 a^2*X+a^2 X a^2*X+a 0 a^2*X+1 a*X+a a^2 a a*X+a a^2*X+a 1 a^2*X a*X a*X+1 1 a*X 1 0 0 1 0 1 a^2*X+a a^2*X+a^2 a a^2*X a a*X+1 a a^2*X+a a^2 0 X+a 0 a*X X+a a^2 X X+a X+1 1 a^2 a*X+1 X+a^2 a*X+a a*X+1 a*X+1 a^2 a^2*X+1 a^2*X+a a^2*X+1 a^2*X+a^2 a^2*X+a^2 X+1 1 a^2*X+a^2 X+1 a*X+a^2 0 a*X+a X+a a^2*X a*X a X a^2*X+a^2 a^2*X+a 0 0 a^2*X a^2*X a*X a^2 a*X a*X+1 a*X+a^2 a X+a X+1 a*X+a X+a 0 a*X 0 0 0 1 a^2 a 1 a*X X+a a X a*X+a^2 a^2*X+1 0 a*X a^2*X a^2*X+a^2 a^2*X+a^2 1 a*X+1 a^2*X+a a*X+a a a^2*X+a a^2*X a^2*X+a a^2*X+1 X X+a^2 X+1 a*X a*X+1 1 a*X+1 a*X+a^2 a X+1 a*X a^2*X+a a*X+a^2 a^2 a^2*X+a^2 a a^2*X+1 a^2*X X+1 X 1 a*X+1 a^2*X+a^2 a a*X+a^2 a*X+a^2 X+a a^2*X+a a 0 X a*X a^2*X+1 a*X+a^2 a^2*X+a a^2*X+a a*X+a^2 1 a 0 0 0 0 X 0 a*X 0 0 0 X X a*X a*X X X a*X a*X X a^2*X a*X a*X a^2*X X X a*X a^2*X 0 0 0 X X a^2*X a*X a^2*X a*X a*X a^2*X a^2*X a^2*X a*X X 0 a^2*X X X a^2*X 0 0 X a*X a*X X a^2*X 0 0 X a^2*X a*X a^2*X a*X a*X a*X a^2*X X X generates a code of length 66 over F4[X]/(X^2) who´s minimum homogenous weight is 178. Homogenous weight enumerator: w(x)=1x^0+276x^178+624x^179+393x^180+960x^181+2088x^182+3348x^183+1503x^184+2508x^185+5412x^186+6780x^187+2133x^188+4320x^189+9672x^190+12840x^191+4050x^192+8076x^193+14424x^194+17724x^195+5694x^196+10272x^197+18108x^198+21540x^199+6078x^200+10728x^201+19032x^202+19860x^203+5202x^204+8160x^205+11376x^206+11424x^207+2619x^208+3276x^209+4644x^210+3684x^211+777x^212+768x^213+900x^214+480x^215+132x^216+84x^217+84x^218+30x^220+21x^224+18x^228+9x^232+9x^236+3x^240 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 273 seconds.