The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 a^2*X 1 a^2*X 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 a*X 1 a*X a^2*X 1 1 1 a^2*X X 1 1 1 1 1 1 1 1 1 1 a^2*X X 0 1 1 1 1 1 1 0 1 a*X 1 1 1 1 a*X 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 a^2 1 a^2*X+a^2 1 1 a^2*X+a^2 a 1 a*X 1 a*X+a^2 1 X+1 1 a^2*X X+1 a^2*X+a a^2*X+a^2 X a^2*X+a a*X a^2 1 1 0 X X+a 1 1 a^2*X+a^2 0 1 X+a^2 X a*X+a a*X+1 a*X+a a^2*X+a^2 a*X+a^2 a*X 1 1 a*X+a^2 X X X+a^2 0 a*X+a^2 1 X+1 1 a^2*X+1 X+1 0 X+a^2 1 0 0 0 1 1 a a^2 1 X+1 1 a 0 X a^2 a*X+a^2 a^2 a*X+a X+1 a^2 0 X+a a X+a^2 X a*X+a X+a^2 a*X X+a^2 X X+a a a^2*X+1 a^2*X+a 1 1 X+a^2 0 a a*X+1 a a*X a*X+a a^2 X X 1 X X+a^2 a*X+a a^2*X+1 a^2 a^2 a^2*X+a 1 1 X+1 a*X+1 X+a^2 X+1 0 a*X+a^2 1 a^2*X+1 X+a^2 X+a X+a^2 a a^2*X a^2*X+a a 0 0 0 0 a^2*X 0 0 0 X X X a^2*X a*X a^2*X a*X a^2*X a*X a*X X a^2*X a*X X X a*X X 0 0 a*X a*X 0 a*X a^2*X X 0 a^2*X a^2*X a^2*X a*X X X a^2*X a^2*X a*X a^2*X 0 a^2*X a*X X a^2*X X 0 X 0 X 0 0 a*X a*X a*X a*X a*X X a^2*X 0 a*X a^2*X a^2*X a^2*X X X a*X 0 0 0 0 X a^2*X a*X X a^2*X a*X a*X X X a*X a*X 0 X a^2*X X a*X 0 X a*X a^2*X X a^2*X a^2*X 0 0 a^2*X a^2*X a*X a^2*X X a*X 0 a*X a*X X 0 a^2*X X a*X X a*X a^2*X a^2*X 0 X X 0 X 0 a*X 0 0 0 a^2*X a*X X a*X 0 0 0 0 a*X 0 X X X generates a code of length 70 over F4[X]/(X^2) who´s minimum homogenous weight is 192. Homogenous weight enumerator: w(x)=1x^0+75x^192+204x^193+108x^194+300x^195+1056x^196+1668x^197+588x^198+864x^199+2028x^200+3240x^201+1212x^202+1224x^203+2976x^204+4404x^205+1488x^206+1644x^207+3258x^208+5364x^209+2052x^210+1716x^211+3936x^212+5160x^213+1980x^214+1848x^215+3375x^216+4944x^217+1284x^218+1152x^219+1869x^220+2148x^221+456x^222+444x^223+678x^224+456x^225+48x^226+24x^227+111x^228+60x^229+24x^232+27x^236+18x^240+9x^244+9x^248+6x^256 The gray image is a linear code over GF(4) with n=280, k=8 and d=192. This code was found by Heurico 1.16 in 20.8 seconds.