The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X a^2*X 1 1 1 1 0 1 1 1 1 0 1 1 1 1 a^2*X 1 1 1 1 1 1 a*X a^2*X 1 1 a*X 1 1 1 1 0 1 1 1 1 1 a^2*X 0 1 X 0 1 1 1 1 a^2*X 1 1 1 0 1 1 0 1 0 0 0 a^2*X 1 a^2*X+a a^2 a^2*X+1 a^2*X+1 a a^2*X+a^2 a^2 1 1 a^2*X+a 1 a^2*X+a^2 a 1 a*X 0 a^2*X+a X+1 1 a^2 a^2*X+a^2 a a*X 1 1 a a^2*X+1 a^2 X+a X 1 1 X+1 a^2*X+a a*X a^2 a^2*X+1 a*X+a a*X 1 a^2*X X+1 a*X a^2 a^2*X+a^2 1 1 a^2*X+a^2 1 a^2*X X+a a*X a*X+1 X X a*X+a X+a^2 a*X+1 1 a^2 1 0 0 1 1 a a^2 1 X+1 1 a 0 X a*X+a a^2 X+1 a^2 X+a^2 a^2 0 a*X+a a a^2*X+a^2 a^2*X X+a a^2*X+1 X+a a^2*X a X+1 X+a X+a^2 a a*X a*X+a^2 X+a^2 a^2*X+a^2 1 0 1 0 a^2*X+1 1 a*X+a X+1 a*X+a^2 a*X+a 0 a^2*X+1 a*X a^2 X+a^2 a*X a^2*X+a^2 a*X+a a^2*X+1 X 1 a*X+a a^2*X a^2*X a*X+a 1 a*X+a^2 a*X a^2*X+1 X+a^2 X+a X+a^2 0 0 0 a^2*X 0 0 0 X X X a^2*X a*X a*X a*X a*X a^2*X a^2*X X a^2*X X X a^2*X a^2*X X 0 0 0 0 a*X a*X 0 X a^2*X 0 a*X a*X 0 a*X 0 a*X X a^2*X a*X a*X a^2*X X a*X X 0 a*X X a*X a^2*X a*X 0 a*X X X X X a^2*X a^2*X a^2*X a*X a*X a*X 0 0 0 0 0 0 X a^2*X a*X X a^2*X a*X a*X X 0 a*X X a*X X a^2*X X a*X a*X X a*X 0 X a^2*X a*X a^2*X 0 a*X a*X X X X a^2*X 0 0 a^2*X a^2*X 0 a*X X X X 0 0 a*X a^2*X a^2*X 0 0 X 0 a^2*X 0 0 0 a^2*X a^2*X a*X a^2*X a*X a^2*X a^2*X a^2*X 0 X 0 generates a code of length 68 over F4[X]/(X^2) who´s minimum homogenous weight is 188. Homogenous weight enumerator: w(x)=1x^0+480x^188+996x^189+372x^190+180x^191+1431x^192+2904x^193+816x^194+384x^195+2427x^196+4620x^197+1320x^198+432x^199+3246x^200+6564x^201+1764x^202+612x^203+3897x^204+6552x^205+2292x^206+708x^207+3891x^208+6288x^209+1704x^210+504x^211+2472x^212+4092x^213+816x^214+216x^215+1251x^216+1524x^217+132x^218+36x^219+216x^220+252x^221+54x^224+36x^228+21x^232+21x^236+9x^240+3x^244 The gray image is a linear code over GF(4) with n=272, k=8 and d=188. This code was found by Heurico 1.16 in 41.4 seconds.