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 X 1 1 1 1 1 1 1 1 0 1 1 2 1 1 1 X 1 X X 0 1 1 0 1 1 1 1 X X 1 X 1 0 0 0 X 0 X 0 0 X X+2 0 2 X X+2 0 X X 2 2 X+2 X+2 2 0 X+2 0 X+2 X+2 X 0 2 0 X+2 X 0 2 X X 0 0 X X+2 2 X+2 2 X 0 2 X+2 X+2 0 0 2 2 X+2 X+2 X X+2 0 X 2 X+2 0 0 X+2 X+2 X+2 X X 2 0 2 2 X X+2 X+2 0 X+2 X X+2 X 0 0 0 X X 0 X+2 X 0 2 X X 0 0 2 X+2 X+2 2 0 X+2 X 2 X X 0 0 X X+2 0 2 2 X X+2 X+2 2 0 2 2 X+2 X X X+2 X+2 0 X 2 2 X+2 0 0 0 X 2 X+2 2 X+2 0 X 0 2 2 X+2 X+2 2 2 0 X+2 2 X 2 X X+2 X+2 2 X 0 X+2 2 0 X 0 0 0 2 0 0 0 2 2 2 0 0 2 2 2 2 0 0 2 2 0 2 0 2 0 0 0 0 0 2 0 2 0 0 2 2 0 0 0 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 0 0 0 0 2 0 2 0 0 2 2 0 0 0 0 2 2 0 0 2 2 2 2 0 0 0 0 2 0 0 0 0 0 0 2 2 2 0 0 0 2 0 0 0 2 0 2 0 2 2 2 2 0 0 2 0 0 2 2 0 2 2 0 2 2 0 2 2 2 2 0 0 2 2 0 0 0 2 2 2 2 0 2 0 2 2 0 2 2 0 2 2 2 2 2 0 2 2 2 0 0 2 0 0 0 0 0 2 0 0 0 2 2 0 2 2 0 0 2 2 2 2 0 0 2 0 0 2 0 2 2 0 2 2 0 2 0 0 2 0 2 0 0 0 2 0 0 2 2 0 2 2 2 2 2 2 2 0 0 2 0 0 2 0 0 2 0 2 0 2 0 2 2 0 2 0 0 0 2 0 2 0 0 0 0 0 0 2 2 2 2 0 2 2 0 2 2 0 2 2 0 2 0 2 0 2 0 0 2 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 2 0 2 0 2 0 0 2 0 2 0 0 2 2 0 2 2 2 2 0 2 2 2 0 2 0 0 0 0 2 2 2 2 generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+237x^72+112x^75+247x^76+256x^77+320x^79+229x^80+224x^81+80x^83+175x^84+32x^85+107x^88+25x^92+2x^96+1x^132 The gray image is a code over GF(2) with n=316, k=11 and d=144. This code was found by Heurico 1.16 in 31.9 seconds.