The generator matrix 1 0 0 0 0 1 1 1 2 1 1 1 1 X 1 X 0 X+2 X 1 1 0 X+2 X+2 1 1 2 1 1 0 1 2 1 2 X+2 1 1 X 1 1 0 1 X 2 1 1 2 X 1 2 1 1 X X+2 X+2 2 1 1 1 X 1 1 0 X+2 X X+2 1 0 0 1 0 X 1 1 X 0 X 1 1 1 2 0 1 1 0 1 0 0 0 0 0 0 0 X+1 2 2 2 2 X+1 1 1 1 1 X+3 1 X+2 1 X+2 X+2 3 1 1 X+3 1 3 1 0 1 1 X+3 X+2 0 1 X+1 1 X 2 1 3 X+1 2 1 X+3 2 X+2 X X 2 1 1 X 3 X+1 X 0 X+2 X X+2 X+2 1 2 1 1 1 1 1 X+1 0 2 1 0 2 3 1 X 1 3 X 0 0 1 0 0 0 1 3 1 2 X 0 X+1 2 X+3 X+3 X+2 X X+2 3 X+1 1 3 1 3 2 X+1 X+3 2 3 X 1 0 1 X 1 X+3 X+2 2 1 X 2 1 X 3 0 1 1 1 1 0 X+1 2 0 X+3 3 X+2 1 X X+2 0 2 1 1 1 1 1 2 0 0 X+2 2 X 3 1 1 X+2 X 0 X 0 X+3 0 X 0 0 0 1 0 1 1 2 3 3 0 X+1 X 1 X+3 X X+1 X+2 1 0 2 X+2 X+1 3 X+3 2 0 3 X X+3 X+1 3 1 X+2 0 X+2 X 1 0 0 1 2 X+3 X+1 1 X+2 X+3 3 X+3 X 2 3 1 X+2 0 X 0 1 1 1 X 1 X X+1 3 3 0 X+1 X+3 X+2 X X+3 X+1 1 X+2 X 1 1 X+1 2 2 1 X X+2 0 0 0 0 1 1 2 1 1 3 X+3 X 0 3 X+1 X+2 X+3 1 2 X+2 X+1 1 0 0 X+1 X+2 3 0 X+3 0 X+2 X+3 X+3 1 1 X 2 0 1 1 1 X+1 1 X X+3 X+2 2 X+3 0 3 3 X+3 3 1 0 2 X+2 0 X X X+3 2 2 X X+1 1 X X+3 X+2 2 0 X X+2 3 2 X+1 1 2 3 3 1 1 X+2 X+1 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 X X+2 X X X X X+2 X X+2 X+2 X X X+2 X X X X+2 X X X+2 X+2 X X+2 X+2 X+2 2 X+2 X X X+2 X+2 X+2 2 X 2 X X+2 X 2 2 X generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+245x^72+662x^73+1414x^74+1768x^75+2753x^76+3828x^77+5185x^78+6410x^79+7999x^80+8502x^81+10194x^82+10532x^83+11406x^84+10658x^85+10849x^86+8830x^87+8249x^88+6322x^89+5211x^90+3484x^91+2621x^92+1622x^93+1006x^94+594x^95+342x^96+200x^97+85x^98+56x^99+16x^100+12x^101+8x^102+6x^103+2x^105 The gray image is a code over GF(2) with n=336, k=17 and d=144. This code was found by Heurico 1.13 in 304 seconds.