The generator matrix 1 0 0 0 1 1 1 1 1 X 1 1 1 1 1 0 X 1 a^2*X a*X 1 1 1 1 1 1 1 1 1 1 1 a*X 1 1 1 a^2*X 1 a^2*X 0 a^2*X 1 1 1 X 1 1 1 1 1 1 1 a*X 1 1 0 1 X X 1 1 1 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 1 1 1 X a^2*X+a^2 a^2*X X+1 0 X a^2*X+a^2 a^2 a*X+a^2 a^2*X+a^2 1 a^2*X+1 0 a 1 a 0 1 a^2*X X a^2*X+a X+1 1 a*X+a^2 a^2*X+a a*X+1 a^2*X+a X+1 1 a^2*X+a^2 1 a*X+1 a^2*X+a^2 a*X a^2*X+a^2 a*X 1 a^2 a*X+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 a^2*X+1 X+a^2 a a^2*X+1 X+1 a^2*X+a^2 X+a^2 a a*X+a a*X+a^2 a^2*X a X a*X a^2*X X+1 1 X X 1 X+1 1 X+a^2 a^2*X+a^2 X+1 a*X+a^2 a^2*X+a^2 a^2*X+a a^2*X+a^2 X a*X+a a^2 a*X+1 a*X+a a*X+a^2 a*X 1 a*X+a 1 a^2*X+a X+1 a^2*X 0 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 a^2*X+a^2 0 a*X+a a^2*X+1 a X a*X+1 a*X+a^2 1 a^2*X+1 a^2*X+a 0 a^2*X+1 a*X+1 a^2*X+a^2 a a*X+a^2 X+a a a^2 a*X X+1 a^2*X+a X+1 a^2*X a^2*X+a a 1 X 1 a^2*X+1 a*X+a^2 a*X a*X+1 X+a X+a^2 X+a^2 a a*X+a X+a^2 X+1 a*X+a X 0 0 0 0 X 0 a*X 0 0 0 X X a*X a*X X X a*X a*X a^2*X a^2*X a*X X a^2*X X a*X 0 a^2*X X X 0 0 X 0 a*X a^2*X a^2*X X a*X 0 X a^2*X 0 a*X X a^2*X 0 0 a*X a*X 0 a*X a^2*X a*X a*X a^2*X X X 0 a^2*X 0 0 generates a code of length 61 over F4[X]/(X^2) who´s minimum homogenous weight is 164. Homogenous weight enumerator: w(x)=1x^0+444x^164+720x^165+876x^166+948x^167+2415x^168+3120x^169+2952x^170+2508x^171+5409x^172+6096x^173+5892x^174+4944x^175+9666x^176+11724x^177+9696x^178+7704x^179+14649x^180+15912x^181+13284x^182+9144x^183+17745x^184+18744x^185+13788x^186+9228x^187+15954x^188+15024x^189+10236x^190+6144x^191+8463x^192+6924x^193+3960x^194+2160x^195+2706x^196+1512x^197+720x^198+228x^199+282x^200+96x^201+36x^202+36x^204+24x^208+15x^212+12x^216+3x^220 The gray image is a linear code over GF(4) with n=244, k=9 and d=164. This code was found by Heurico 1.16 in 227 seconds.