The generator matrix 1 0 0 1 1 1 X X+2 1 1 X+2 1 1 2 1 X^2 1 X^2+2 1 1 X 1 1 X^2 1 X^2+2 2 1 X^2+X 1 X^2+X 1 1 2 X+2 1 1 X^2+X+2 X+2 1 1 1 X^2+X+2 X+2 X^2+2 1 1 X 1 1 1 1 2 X+2 1 X^2+X+2 1 1 X^2+2 1 1 1 X^2+X+2 1 X^2+X 1 2 X^2 1 1 1 1 1 X+2 1 1 1 0 2 X 0 1 X^2+X+2 1 1 X^2+X 1 0 1 X+2 2 X^2+X 0 1 X 1 0 1 0 0 X^2+1 X+1 1 2 0 X+3 1 2 X^2+1 1 0 1 3 1 1 X^2+X X+2 X^2+2 X+1 X^2+X+2 X^2+X+2 1 1 X^2+X+3 1 1 1 X^2+3 X 1 X X^2+2 X^2 1 X^2 X^2+X X+3 3 0 1 1 X+1 X^2+X+2 2 X^2 X^2+X+3 X^2+3 0 1 1 X^2+X 1 X^2+1 X^2+X+2 1 X^2+X+2 X^2+1 X+2 X+2 X+1 1 X 1 X^2 X^2+X+2 X^2 X 0 1 1 2 2 X^2+X+3 1 2 1 X X^2 X+2 X^2 X^2+X+2 X^2+X 3 X 2 1 1 1 1 X^2 1 X^2+2 0 0 1 1 1 0 X^2+1 1 X 1 X 1 X X^2+X+1 X^2+X X^2+2 0 X^2+X+3 X+3 X^2+X+3 1 2 X^2+X+1 1 X^2+3 X+2 1 X X^2+1 X^2+1 X^2 0 X^2+X+2 3 1 X+1 X^2+3 2 1 X X^2+3 X+1 1 X^2+1 X^2+2 0 X^2+X+3 1 X^2+X+1 X+2 X X+2 X^2+X+2 X+1 X^2 X^2+X 2 1 0 X^2+X+3 X^2 X^2 1 X^2+2 2 X^2+2 X^2+1 1 X+2 1 X^2+1 X^2+X+2 X+1 X^2+X+2 X^2+2 X X+1 X^2+3 1 X^2 1 2 1 X^2+3 X+1 1 3 1 X^2 X^2+X X^2+X+1 X^2+X+3 0 X^2+X+2 1 X^2+2 0 0 0 X X+2 2 X+2 X+2 X+2 0 X 2 X 2 2 X^2+X X^2+X+2 X+2 X^2+X X+2 2 X X^2 X+2 2 X^2 X^2 2 2 X^2+2 X X^2 X X X^2+X+2 X^2+2 X^2+X 2 2 X^2 X X^2 X^2+X+2 X^2+X X^2+2 X+2 X^2+2 X^2+2 X X^2+X+2 0 X^2+2 X^2+X+2 0 X^2+X+2 X^2+2 0 X X 0 X 2 X+2 X^2+2 X^2+2 X X^2+X X^2 2 X^2+2 0 X+2 X+2 X^2+X+2 X^2 X^2+X 0 X^2 X X^2+X X^2+X+2 2 X^2+X+2 X^2+2 X^2+X+2 X^2 0 X^2 X^2+X+2 2 X^2+X 0 X 2 X X+2 generates a code of length 96 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 89. Homogenous weight enumerator: w(x)=1x^0+200x^89+1160x^90+1616x^91+2465x^92+2740x^93+3413x^94+3326x^95+4038x^96+3218x^97+3128x^98+2376x^99+1948x^100+1100x^101+958x^102+446x^103+252x^104+142x^105+109x^106+56x^107+38x^108+8x^109+23x^110+4x^111+1x^114+1x^116+1x^120 The gray image is a code over GF(2) with n=768, k=15 and d=356. This code was found by Heurico 1.16 in 15.9 seconds.