The generator matrix 1 0 1 1 1 X+2 1 1 2 1 X 1 2 1 1 1 X+2 1 X 1 1 1 1 0 1 2 1 2 1 1 X 1 1 1 1 X 1 2 1 X+2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 X+2 X+2 2 X 2 1 0 0 1 1 1 1 1 1 1 2 1 1 0 2 0 X+2 X 1 1 0 1 1 0 1 1 X X+3 1 X+2 1 X+3 1 0 X+1 3 1 2 1 X+2 X+1 3 X 1 0 1 X+1 1 0 X+1 1 X 1 X+1 0 1 2 1 X+2 1 3 3 X+2 1 X+2 1 1 3 X+1 X+2 0 X+1 2 X+2 1 1 1 1 X X+1 1 1 2 X+2 1 X+1 1 0 X+2 1 2 X+1 0 X 1 1 1 X+2 2 0 0 X 0 0 0 0 0 0 2 2 X+2 X X 2 X X X X+2 X X 0 X+2 X 0 X+2 X+2 2 X 0 X+2 X 2 2 X+2 2 2 X+2 2 2 X+2 2 X+2 X X+2 2 X+2 X 0 0 X+2 2 X+2 X+2 X+2 0 0 2 X 0 0 X+2 X 0 X X 0 X+2 2 X+2 X X 0 2 2 X+2 X X+2 0 0 0 0 X 0 0 X 2 X 2 X+2 2 X+2 2 X X+2 0 X X 0 X X+2 X+2 0 X 0 0 2 X 2 2 2 X X 2 0 X X+2 X 2 X+2 0 X 0 0 2 X 2 2 0 X+2 X+2 X X+2 0 X+2 X+2 X+2 X+2 X+2 2 X+2 2 0 X+2 2 2 X 2 0 0 0 X X X+2 2 2 X+2 0 0 0 0 0 X 0 0 X+2 2 0 2 2 X+2 X X+2 2 X X X X 0 X X X+2 X+2 2 X+2 X 0 0 0 0 2 2 2 X+2 0 0 X X+2 2 X+2 0 X X X 0 2 2 X 2 X X+2 0 X X+2 0 0 0 0 2 X X+2 X X X X X+2 X 0 0 2 X 2 X+2 2 0 0 X 0 0 0 0 0 2 0 0 2 0 2 0 2 0 0 0 2 0 2 0 2 2 2 0 2 0 2 2 0 0 2 0 0 2 2 0 2 0 0 2 0 2 2 0 2 2 2 2 0 2 2 2 0 0 2 2 2 0 2 0 2 0 0 0 0 2 0 2 2 2 2 2 2 2 0 2 0 0 2 0 0 0 0 0 0 2 2 0 2 2 2 2 0 0 2 2 2 0 2 2 0 2 2 2 0 0 2 2 0 0 2 0 0 0 2 2 0 2 0 0 2 0 0 0 0 0 0 2 2 2 2 0 0 0 0 2 0 2 0 2 0 2 2 0 0 2 2 2 0 2 2 2 2 2 0 0 2 2 generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+31x^68+110x^69+212x^70+310x^71+523x^72+688x^73+765x^74+1026x^75+1207x^76+1236x^77+1471x^78+1464x^79+1320x^80+1390x^81+1177x^82+940x^83+785x^84+600x^85+373x^86+228x^87+172x^88+108x^89+78x^90+56x^91+49x^92+20x^93+15x^94+6x^95+7x^96+6x^97+3x^98+2x^99+2x^101+1x^102+1x^104+1x^106 The gray image is a code over GF(2) with n=316, k=14 and d=136. This code was found by Heurico 1.16 in 19.8 seconds.