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 X^2 1 X^2 1 1 X 1 1 1 1 X 1 1 X 1 X 1 1 1 X^2 X 1 X^2 X 1 X^2 X 0 0 X^2 0 X 1 1 X 1 1 0 X 1 1 X 0 X 0 0 0 X X^2+X X 0 X^2 X^2 0 X X^2+X X X^2+X X^2+X X^2+X X^2+X X^2 0 0 X^2+X X^2 X^2+X 0 X^2 X X X^2 X 0 X X X^2+X X X^2+X X^2+X X^2 X^2 X X^2 X^2 X X 0 X^2+X X^2+X X^2 X^2 0 0 X X 0 X X^2+X X^2 X X X X X 0 0 X 0 X^2+X X^2 X^2 X X X^2+X X^2+X 0 0 0 X 0 X X X^2+X 0 0 0 X^2+X X^2+X X X X^2 0 X X^2 0 X^2+X X^2+X X^2 X^2+X X^2 0 X^2 X X^2 X X X X^2 X 0 0 X^2+X 0 X X X X^2 X X^2+X X X^2+X 0 X 0 0 X^2 0 X^2 X X^2 X^2+X X^2 0 X^2 X X X^2+X X^2+X X^2+X X X X 0 X X^2 X 0 X^2 X^2+X X X^2 0 0 0 X X 0 X^2+X X X^2 X^2+X X X^2 X^2 X X X^2 0 X^2+X 0 X X^2 X X 0 0 X X^2 X^2+X X^2+X X X X^2 X^2 X 0 X^2 X^2+X X^2 0 X^2 X^2+X 0 X^2+X 0 0 X X X^2 X X^2+X X^2+X X 0 X X 0 X^2 0 X^2+X 0 X X^2+X 0 0 X^2+X X^2 0 X X X X 0 X X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 0 X^2 X^2 0 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2 0 0 0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 generates a code of length 75 over Z2[X]/(X^3) who´s minimum homogenous weight is 66. Homogenous weight enumerator: w(x)=1x^0+110x^66+4x^67+276x^68+56x^69+330x^70+132x^71+401x^72+196x^73+516x^74+236x^75+448x^76+212x^77+371x^78+140x^79+260x^80+44x^81+125x^82+91x^84+4x^85+71x^86+46x^88+13x^90+12x^92+1x^108 The gray image is a linear code over GF(2) with n=300, k=12 and d=132. This code was found by Heurico 1.16 in 1.8 seconds.