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 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 X^2 1 X 1 1 X 1 X^2 X^2 1 0 X^3+X^2 0 0 0 X^2 X^3+X^2 X^2 0 0 0 0 X^2 X^3+X^2 X^2 X^3+X^2 0 0 X^2 X^2 X^3 0 X^2 X^3+X^2 X^3 X^2 X^2 X^2 X^3 X^3 0 X^3+X^2 X^3 0 X^3 X^2 0 X^2 X^3+X^2 X^2 X^3 X^3 X^2 X^3+X^2 0 X^2 X^3+X^2 X^3 X^3 0 X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2 0 X^2 X^3 X^3 X^3+X^2 X^3+X^2 0 X^2 0 X^2 X^3+X^2 X^3+X^2 X^3 0 X^2 X^3 0 X^3 X^3 0 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^3+X^2 0 0 0 X^3+X^2 0 X^2 X^2 X^3+X^2 0 X^2 0 0 X^3+X^2 X^2 X^3+X^2 0 0 0 X^2 X^2 0 0 X^2 X^3 X^2 X^3 0 X^3 X^3+X^2 X^2 X^2 X^3 X^3+X^2 0 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^2 X^3 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 0 X^3+X^2 X^2 0 X^3 0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 0 X^3 0 X^3 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^2 0 0 X^3+X^2 X^2 X^3 0 X^3+X^2 X^2 0 X^3 X^2 0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 0 0 0 X^3+X^2 X^2 0 X^3+X^2 X^2 X^2 0 X^3+X^2 0 0 X^3+X^2 X^2 0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 0 X^3 X^2 0 0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 0 X^3 X^2 X^2 0 X^3 X^3+X^2 X^3 X^2 X^3+X^2 0 X^3 X^2 X^3+X^2 0 X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 0 X^3+X^2 X^2 0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 0 X^3+X^2 X^3 X^3 0 0 X^3 X^3 0 0 0 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 0 X^3 X^2 X^3 X^3+X^2 X^2 X^3 0 0 0 0 X^3 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 0 0 0 0 0 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 0 0 0 0 0 0 0 X^3 X^3 X^3 X^3 X^3 X^3 0 0 X^3 X^3 X^3 0 0 X^3 X^3 X^3 X^3 0 0 0 X^3 0 0 0 X^3 0 X^3 X^3 0 0 X^3 0 X^3 0 0 X^3 0 X^3 0 X^3 0 0 X^3 0 0 generates a code of length 87 over Z2[X]/(X^4) who´s minimum homogenous weight is 82. Homogenous weight enumerator: w(x)=1x^0+112x^82+8x^83+145x^84+128x^85+398x^86+496x^87+395x^88+128x^89+130x^90+8x^91+57x^92+26x^94+8x^96+6x^98+1x^100+1x^164 The gray image is a linear code over GF(2) with n=696, k=11 and d=328. This code was found by Heurico 1.16 in 95.3 seconds.