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 2 2 2 2 2 2 2 1 1 2 2 1 1 2 0 1 1 0 2 1 2 1 1 1 2 1 1 0 1 2 1 2 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 2 0 2 2 2 2 0 2 0 2 0 0 0 2 2 0 2 2 0 0 2 0 2 2 0 2 2 2 0 2 0 2 0 0 2 0 0 0 2 0 0 2 0 2 0 0 2 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 0 2 0 0 0 2 2 2 0 0 0 2 0 0 0 2 0 0 2 2 0 0 2 0 2 0 0 0 2 2 2 2 0 2 0 2 0 0 2 2 2 2 0 2 0 0 0 0 0 2 2 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 0 0 0 2 2 0 2 2 0 0 0 2 0 0 0 2 0 2 2 0 0 2 0 0 2 2 0 2 2 2 2 0 2 0 2 2 2 2 2 2 0 2 2 2 2 2 0 2 2 2 2 2 2 2 0 2 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 0 2 2 0 2 2 0 0 0 0 2 2 2 2 0 0 0 2 2 0 0 0 0 0 0 2 2 2 2 0 0 0 2 0 2 2 2 0 0 2 0 0 2 0 2 0 2 2 0 0 0 0 2 2 0 0 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 2 0 2 2 0 2 0 2 0 2 2 0 2 2 0 0 0 0 0 0 2 2 0 0 0 0 2 0 2 2 2 0 2 2 2 0 0 0 2 2 0 2 0 0 0 0 0 2 0 2 2 0 0 2 2 0 0 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 2 0 2 0 2 0 0 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 2 2 2 2 0 2 2 2 0 0 0 0 0 2 0 0 2 2 0 2 0 2 0 0 0 0 0 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 2 2 0 2 0 0 0 2 2 2 2 2 2 0 2 0 2 2 2 0 0 2 0 2 2 0 2 0 2 2 2 0 0 0 2 0 2 2 0 0 0 2 0 0 2 2 2 0 2 0 0 2 2 0 2 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 2 0 0 2 0 2 0 0 2 0 0 2 0 2 2 2 0 2 2 2 0 2 2 2 0 2 2 0 2 0 2 0 2 2 2 2 2 2 0 2 0 2 0 0 0 2 0 0 2 0 2 2 0 0 2 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 0 0 2 0 0 2 2 0 0 2 0 2 0 0 2 2 0 2 2 2 2 0 0 2 2 2 0 2 2 0 2 2 0 0 0 2 0 2 0 0 2 0 2 0 0 0 0 2 0 2 2 0 2 0 0 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 2 0 0 0 2 0 0 0 0 0 2 0 2 2 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 2 0 0 2 2 2 2 0 2 2 2 2 2 2 0 0 2 2 0 0 2 2 2 0 0 generates a code of length 82 over Z4 who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+159x^68+2x^70+322x^72+76x^74+463x^76+242x^78+618x^80+392x^82+643x^84+230x^86+409x^88+76x^90+243x^92+6x^94+143x^96+58x^100+9x^104+2x^108+1x^112+1x^128 The gray image is a code over GF(2) with n=164, k=12 and d=68. This code was found by Heurico 1.16 in 6.06 seconds.