The generator matrix 1 0 0 0 1 1 1 0 0 X^2 X^2 1 1 1 1 1 X^2+X X^2+X 1 1 1 X X^2 1 1 1 1 0 0 X^2+X 1 X^2 X^2 1 X^2+X 1 1 X X^2 1 0 X X^2+X 0 1 1 1 1 0 1 1 1 1 X^2+X X^2 1 1 0 X 0 X^2+X 1 1 X^2+X X^2 X^2+X 1 X 1 X^2 1 X^2+X 1 1 X 1 1 X^2+X 1 X 1 1 X^2+X 1 X 1 1 X^2 1 1 X^2+X 1 1 1 1 0 1 0 1 0 0 0 1 1 1 X^2 1 1 0 1 1 0 X X 1 X^2+1 X^2+X X^2 1 X^2 0 X^2+X+1 X+1 X+1 1 1 X^2 X 1 X X^2+X+1 1 X^2+X 0 1 0 X^2+X+1 1 X X^2 1 X^2 X^2+X+1 X^2 1 1 X^2+1 X 1 X^2+X 1 X X^2+X+1 X^2+1 1 1 1 1 X^2+1 X^2+X+1 X^2 X 0 X 1 X X^2+X X+1 X^2+X 1 0 1 X^2+1 1 1 X^2+1 0 X^2+X+1 X^2+X 1 X^2+1 1 X^2+X+1 X^2 X^2 X+1 X^2+X X^2+X X^2+1 X^2 X^2+1 X^2+X+1 1 0 0 0 1 0 1 X^2 X^2+1 1 1 0 1 X^2 1 0 X^2+1 X^2 1 X X^2+X X^2+1 X 1 X X^2+X+1 X^2+1 0 X^2+1 X X^2+X+1 1 X^2+X X 1 X^2+X 0 X^2+1 X+1 X+1 1 X^2+1 X^2 1 X^2 X X^2+X+1 X X^2+1 X^2 X^2+1 X^2+X+1 X+1 0 1 1 0 X^2+X+1 X^2+1 1 X^2+1 X^2+X+1 X^2 X^2+X+1 X 1 1 X^2+X X^2 X+1 X^2+X+1 1 X^2+X+1 1 X^2+X X X^2+X+1 X^2+X X X^2 X^2+X 1 1 X^2+1 X^2+X+1 X^2+X+1 X^2+1 X+1 X^2 1 X^2+X+1 X^2 1 1 X+1 X^2 X X+1 0 0 0 0 1 X^2 0 X^2 X^2 1 1 X^2+1 1 1 X^2+1 X^2+1 X^2+X X+1 X^2 0 0 X+1 X 1 X+1 X^2+X X^2+X+1 1 1 X+1 X^2+X X X^2+X+1 0 1 0 X X^2+1 0 X^2+X+1 X^2 X^2+X+1 0 1 X 0 0 X^2+X+1 X+1 X^2+X X X^2 X X^2+1 X^2+1 1 X^2+1 X^2+X X+1 X^2+X+1 X^2+1 X^2+X 1 X X^2 X^2+X+1 1 X^2+X+1 X^2+X 1 1 X^2 1 X^2+X+1 X X+1 X^2+1 0 X^2+X+1 X 0 X+1 X+1 X 0 X^2 X^2+X X^2+X+1 1 X 1 X^2+X X 1 X^2+1 1 X^2+X 1 generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 90. Homogenous weight enumerator: w(x)=1x^0+50x^90+254x^91+312x^92+486x^93+350x^94+408x^95+319x^96+350x^97+254x^98+264x^99+193x^100+176x^101+109x^102+140x^103+71x^104+110x^105+63x^106+50x^107+27x^108+46x^109+17x^110+20x^111+17x^112+5x^114+4x^116 The gray image is a linear code over GF(2) with n=388, k=12 and d=180. This code was found by Heurico 1.11 in 0.64 seconds.