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 a^2*X 1 a*X 1 a*X X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1 1 a*X 1 1 1 1 1 1 1 0 1 1 a*X 1 1 1 1 X 1 1 1 a^2*X 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 1 a*X+a^2 a^2*X 0 1 1 a X+1 X+a a*X+1 a^2*X a^2*X+1 0 a^2*X+a^2 X+a a^2*X+a^2 a^2*X a^2*X+a^2 X+a X a^2*X+a^2 1 a*X 1 X+1 a^2*X+1 X+a^2 1 a^2 a^2*X a*X+a X+a a*X+a^2 a*X+a a*X+a 1 1 a*X+1 1 1 a*X+a^2 a*X a*X+a^2 a^2*X X+a^2 a^2 0 X 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 X+a a 0 a*X+1 1 X+a X+1 a*X+a^2 a^2 a^2*X X+a 1 a a^2*X+a^2 X+a^2 a^2 a*X+1 a^2*X a^2*X a^2*X a^2*X+a^2 X a*X+a a*X a^2 X+a^2 X+a X+a X a*X+a a a^2*X+1 a^2*X+1 1 1 a a*X+a a*X+a^2 a^2 X+a^2 a a*X+1 X+1 a^2*X+1 a^2*X 1 1 a^2*X+1 a*X 1 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 a*X X a*X a^2*X a^2*X X a*X 0 X a*X X a*X a*X 0 X 0 0 0 a*X 0 X a^2*X X X 0 0 X a^2*X a*X a*X a^2*X a^2*X a^2*X a^2*X a*X X a^2*X X X a*X a^2*X a*X 0 X a^2*X a^2*X X a*X X a^2*X 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 0 0 a^2*X X X a*X X a*X a^2*X 0 0 a^2*X 0 0 a*X 0 X a*X a^2*X a^2*X 0 a*X X 0 a*X a^2*X 0 a*X 0 X a*X X a*X a^2*X a^2*X 0 a*X X X a*X a^2*X 0 X a*X 0 0 0 a*X a^2*X generates a code of length 69 over F4[X]/(X^2) who´s minimum homogenous weight is 190. Homogenous weight enumerator: w(x)=1x^0+276x^190+432x^191+489x^192+264x^193+1428x^194+1200x^195+1320x^196+588x^197+2844x^198+2220x^199+2292x^200+984x^201+4128x^202+3324x^203+3084x^204+1176x^205+4452x^206+3684x^207+3420x^208+1272x^209+4824x^210+3576x^211+3147x^212+1020x^213+4116x^214+2724x^215+1977x^216+648x^217+1824x^218+1020x^219+459x^220+192x^221+600x^222+252x^223+96x^224+84x^226+27x^228+24x^232+15x^236+18x^240+6x^244+3x^248+6x^252 The gray image is a linear code over GF(4) with n=276, k=8 and d=190. This code was found by Heurico 1.16 in 20.6 seconds.