The generator matrix 1 0 1 1 1 X+2 1 1 0 X+2 1 1 1 1 X 1 2 1 X+2 1 1 X+2 1 1 1 1 X 1 2 1 1 X 1 2 1 X+2 1 1 1 1 1 X 1 0 1 1 0 1 1 2 1 1 X X X 0 1 1 0 1 1 X+2 1 1 X 1 X 1 1 1 2 1 X+2 1 1 1 X+2 X 1 1 2 1 0 1 1 0 1 1 X X+3 1 1 X+3 2 X X+1 1 X 1 1 1 3 0 1 X+3 X 2 0 1 X+3 1 X+1 X+3 1 X+2 1 X 1 3 3 X+3 X+2 X+2 1 X+1 1 3 X 1 3 3 1 0 0 1 1 1 1 X+3 1 1 X+2 1 1 X 1 1 X+1 1 0 X+1 0 2 1 1 2 2 X 1 1 X X+1 2 2 0 0 X 0 0 0 0 0 0 2 X+2 X X+2 2 0 X X X X+2 2 X+2 X+2 X X X 0 X+2 X 2 2 X X+2 X X+2 2 X X 0 2 2 2 0 2 0 2 X 0 2 X+2 X+2 X 0 0 0 X X X+2 X+2 X X 0 X X X+2 X X+2 2 X 2 2 X 2 X+2 0 X 2 X 2 2 2 2 X 0 0 0 X 0 0 X 2 X X+2 0 X+2 X X 0 0 2 X X+2 X+2 2 0 X 2 X+2 X X+2 X+2 X+2 2 2 0 X X+2 2 0 0 2 2 0 X+2 X+2 X+2 X X+2 0 0 2 X 2 X+2 0 2 X+2 2 0 X 2 X X 2 X 2 X+2 X+2 X 2 2 X 2 0 X 2 X X+2 X 2 2 X+2 X+2 2 2 0 0 0 0 X 0 0 X+2 X+2 X+2 2 X X X+2 X X+2 0 0 0 X X+2 0 2 2 2 X X X+2 0 0 X+2 X+2 2 0 X+2 X X+2 X X 2 X+2 2 X+2 2 0 X X 2 0 0 X X X+2 X X+2 X+2 2 X+2 X X 0 X 0 2 0 X 2 0 X+2 0 2 X+2 X 2 X+2 X 0 0 X 0 X X 0 0 0 0 0 2 0 0 0 0 0 0 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 2 2 2 2 2 2 0 2 0 2 2 2 2 2 2 2 2 2 0 2 2 2 2 0 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 2 2 0 2 0 2 2 2 2 2 0 2 0 0 0 2 0 2 0 2 2 0 0 0 2 0 0 0 0 0 0 2 2 2 0 0 2 0 0 2 2 2 2 2 2 0 0 2 0 0 2 0 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 0 2 0 2 2 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+222x^72+68x^73+537x^74+264x^75+894x^76+596x^77+1252x^78+932x^79+1502x^80+1204x^81+1677x^82+1236x^83+1467x^84+916x^85+1127x^86+588x^87+784x^88+280x^89+378x^90+52x^91+179x^92+8x^93+105x^94+62x^96+44x^98+6x^100+1x^104+2x^108 The gray image is a code over GF(2) with n=328, k=14 and d=144. This code was found by Heurico 1.16 in 49.1 seconds.