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 2 X X X 2 1 1 0 0 0 1 1 X 1 0 1 1 X 0 2 1 1 1 1 1 X 1 1 0 1 1 X X 1 X X 0 1 X X 1 X 1 1 1 0 X 0 0 0 0 0 0 2 2 X X+2 X 0 0 2 X+2 X+2 X X X X 0 X X+2 X 0 X X+2 2 X+2 2 2 X+2 X 0 0 X 2 2 X+2 2 X X X 2 2 X X X+2 X X+2 X 0 X+2 X+2 2 0 X+2 X+2 2 0 2 X 2 0 2 2 2 X+2 2 2 X X+2 2 X 0 0 2 0 2 0 2 0 0 X 0 0 0 0 0 0 0 0 0 2 X+2 X+2 X+2 X X+2 X+2 X 2 2 X+2 X+2 0 0 X X X X+2 X+2 X+2 2 2 X+2 X X 2 2 X X 0 X 2 0 2 0 X 0 X 2 X 2 X+2 X 0 X X X X X+2 2 X+2 X 2 2 2 2 X+2 X+2 X 2 X X X 2 0 2 X 2 X X 0 0 0 0 X 0 0 2 X+2 X X X X 2 X+2 X 2 2 0 2 2 2 2 2 X X+2 X 2 X X+2 X+2 X X+2 0 2 0 0 0 X+2 2 X X+2 0 0 0 0 X X X+2 X+2 X+2 0 X 2 0 X X 0 X 2 0 0 X+2 2 X 0 X X 0 X X+2 X+2 0 0 0 X 0 X 0 2 X X 0 X+2 0 0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 X X 0 2 X 0 X+2 X+2 X X+2 X 2 2 X 2 2 0 X+2 2 0 X+2 X X+2 2 0 X 0 0 2 0 X X X+2 0 X X X 0 2 X+2 2 0 0 X+2 X X X 2 2 X 0 X+2 X+2 X+2 2 X+2 X 2 X X+2 X+2 X 2 2 X 2 X+2 0 2 X 0 0 0 0 0 X X 2 X+2 X X+2 2 X X 0 X 0 X+2 X+2 0 X 2 2 X+2 2 X X+2 X+2 2 X 2 2 X+2 0 X X+2 0 0 X X 0 X+2 2 2 X+2 2 2 X+2 X X+2 2 X X+2 X X+2 X+2 2 2 0 X 2 2 0 0 0 0 X 2 X+2 2 0 0 2 2 0 0 2 X X+2 2 X X+2 X generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+48x^72+112x^73+150x^74+228x^75+287x^76+330x^77+398x^78+456x^79+547x^80+642x^81+672x^82+698x^83+671x^84+598x^85+506x^86+418x^87+345x^88+240x^89+204x^90+178x^91+130x^92+90x^93+66x^94+62x^95+41x^96+30x^97+18x^98+8x^99+8x^100+6x^101+2x^102+1x^104+1x^120 The gray image is a code over GF(2) with n=332, k=13 and d=144. This code was found by Heurico 1.16 in 7.98 seconds.