The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1 1 1 1 X X 1 1 X 1 X 1 1 1 X X 0 X 0 0 0 0 X X X a*X 0 X a^2*X X a^2*X a^2*X a^2*X a*X X a^2*X 0 a^2*X a*X X 0 a*X X 0 0 a^2*X a^2*X a^2*X a^2*X 0 a*X a*X a*X 0 a^2*X a*X a*X 0 a*X a^2*X 0 a*X X X 0 X X X a*X X 0 X X a^2*X a^2*X X 0 a*X a*X a^2*X a^2*X a*X a*X a*X a^2*X a^2*X X a*X a^2*X 0 a^2*X 0 a*X a*X 0 a^2*X X a^2*X X X X a^2*X X a^2*X X X 0 a*X 0 0 0 0 X 0 0 X a^2*X a*X a*X a*X 0 0 a*X X 0 0 a^2*X 0 a*X a*X a*X a*X a^2*X a^2*X X X 0 a^2*X X a^2*X 0 a^2*X a*X a*X X 0 0 a^2*X 0 0 a*X a*X X a*X X X X X a*X a^2*X a*X a^2*X a^2*X a*X a*X X X 0 a*X 0 a^2*X X a^2*X X X a^2*X a*X a*X X X 0 a*X a*X X X X 0 0 a*X 0 X 0 X a^2*X a*X X X X a*X X a*X X a*X 0 0 0 0 X 0 a^2*X 0 X a*X a^2*X X X X X 0 a*X 0 a*X 0 a^2*X a^2*X X X a^2*X a^2*X a^2*X a*X a^2*X 0 a*X a*X a*X a^2*X a*X X a^2*X X X a^2*X a^2*X a*X 0 a^2*X 0 a*X X X 0 a*X 0 a*X a*X a*X 0 X X a*X a^2*X 0 X a^2*X a*X X a^2*X a*X a^2*X X a*X 0 0 a*X a^2*X a^2*X a*X a^2*X X 0 a*X 0 X a^2*X 0 a^2*X a*X a^2*X a^2*X a^2*X a*X a^2*X a*X a^2*X a*X a^2*X X 0 0 0 0 X X X a^2*X X X X a*X 0 a*X X a^2*X a^2*X a*X a*X 0 a*X a^2*X a^2*X a^2*X a^2*X a^2*X a*X a*X a*X 0 0 X X a*X a^2*X X X 0 a*X a*X a^2*X X X X a*X 0 a^2*X 0 a^2*X a^2*X 0 a*X 0 a^2*X a^2*X X 0 0 a*X 0 0 0 X a^2*X a^2*X a^2*X 0 a*X a*X X 0 0 a*X a^2*X X 0 X 0 a^2*X a*X 0 a*X a*X 0 a^2*X a*X X X a^2*X a*X X a^2*X 0 a^2*X generates a code of length 94 over F4[X]/(X^2) who´s minimum homogenous weight is 268. Homogenous weight enumerator: w(x)=1x^0+186x^268+24x^269+150x^272+240x^273+162x^276+480x^277+117x^280+912x^281+126x^284+1032x^285+66x^288+384x^289+48x^292+48x^296+15x^300+18x^304+9x^308+33x^312+18x^316+6x^320+9x^324+3x^328+3x^336+3x^344+3x^348 The gray image is a linear code over GF(4) with n=376, k=6 and d=268. This code was found by Heurico 1.16 in 3.72 seconds.