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 2 X X 1 X X 1 X X X 1 1 1 1 1 2 1 1 0 1 2 2 1 1 1 1 0 1 X X 0 X 2 1 X X 1 1 2 1 X 0 X 0 0 0 0 0 0 0 X+2 X X X X X+2 X+2 X 2 X 0 X 2 0 X+2 X 2 X X+2 2 2 2 X+2 X+2 2 0 0 X+2 2 2 0 X+2 X X X 0 X+2 X 2 X+2 0 X X X+2 X+2 X+2 X 0 X+2 X 2 0 2 X 2 X+2 X 2 X X X 0 X 2 2 X X+2 X 0 X+2 X 0 X+2 0 0 X 0 0 0 X X+2 X 2 X X+2 0 0 X X+2 2 2 2 X 2 X 2 X X+2 X X X+2 2 X 0 0 0 X+2 X X X+2 X 2 0 X 2 2 0 2 2 X+2 0 0 X+2 X+2 0 X+2 0 X+2 X 0 X+2 X 2 0 X 2 2 X 0 0 X X 2 X 2 X 2 X+2 0 2 X+2 0 0 2 2 0 0 0 X 0 X X X 0 X+2 2 X X+2 0 0 X+2 X+2 X+2 X X+2 0 2 2 X 0 X 0 X 2 X X X 0 0 2 2 2 X 0 0 X+2 0 X 2 X X+2 0 0 X+2 2 0 2 X+2 0 X 2 X X 0 2 2 X+2 2 X+2 0 X 2 0 0 2 X+2 2 X 0 X+2 X+2 2 X+2 2 0 2 2 0 0 0 0 X X 0 X X+2 X 0 X 2 X+2 X 2 2 0 X+2 X 2 0 2 X 0 X+2 X 0 2 2 X+2 2 X+2 2 X+2 X+2 X+2 2 2 X X X 2 X+2 2 X+2 0 X+2 X+2 2 2 0 X X+2 0 0 X+2 0 X+2 X 2 X+2 X 0 0 0 2 X 2 X+2 2 X 2 X 2 2 2 2 X+2 X 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 2 2 2 2 2 2 0 0 2 2 2 2 0 2 2 0 2 2 2 2 0 2 2 2 2 0 2 0 0 2 2 0 0 2 2 2 0 2 0 2 0 2 2 2 2 2 2 2 2 0 0 2 0 0 2 2 0 2 0 0 2 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 2 0 2 2 2 2 2 2 0 0 0 0 0 2 0 2 2 0 2 0 2 0 2 0 2 2 2 0 2 2 2 2 0 0 0 2 0 0 2 0 2 2 2 2 0 2 0 0 2 2 0 2 0 2 2 0 2 2 2 0 0 2 2 0 0 0 0 generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72. Homogenous weight enumerator: w(x)=1x^0+214x^72+16x^73+402x^74+52x^75+581x^76+128x^77+676x^78+372x^79+886x^80+456x^81+866x^82+452x^83+831x^84+368x^85+582x^86+140x^87+439x^88+56x^89+288x^90+8x^91+185x^92+106x^94+51x^96+20x^98+11x^100+4x^102+1x^120 The gray image is a code over GF(2) with n=328, k=13 and d=144. This code was found by Heurico 1.16 in 45.7 seconds.