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 X 1 1 X X 1 1 1 X X 1 X X 1 1 1 1 1 1 1 X X X 2 1 X 1 1 X 1 1 1 X 2 X 1 1 1 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 0 2 2 2 0 2 2 0 0 2 0 0 2 2 0 2 2 0 2 2 0 2 0 0 2 0 2 2 0 0 0 0 2 2 2 2 2 0 2 2 0 2 0 2 2 2 2 2 0 0 0 2 2 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 2 0 2 2 2 2 2 2 2 0 2 0 2 0 2 2 0 2 0 0 2 0 0 0 0 2 2 2 2 2 0 0 2 2 0 0 0 2 0 0 0 0 0 0 0 0 2 2 2 2 2 0 2 2 2 2 0 0 2 2 2 2 2 2 0 2 0 2 2 0 2 0 0 0 0 2 0 0 2 0 0 0 0 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 2 0 0 0 2 0 0 2 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 0 2 2 2 0 2 0 2 0 2 0 0 2 0 2 0 0 0 0 0 2 2 0 0 2 0 2 0 0 2 2 0 0 2 2 2 2 2 2 0 2 0 2 2 2 2 0 0 0 2 2 2 2 0 2 2 0 0 0 2 2 2 2 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2 2 2 2 2 0 0 2 2 0 0 0 2 0 0 0 2 2 0 2 2 0 2 2 2 2 0 0 2 0 2 0 0 2 0 0 0 0 0 2 2 2 0 0 0 2 0 2 0 2 2 0 0 2 0 2 0 0 0 0 2 2 2 2 2 2 0 0 0 0 0 0 2 0 0 0 2 0 0 0 2 2 0 0 2 0 0 2 2 0 2 2 2 0 2 2 2 0 0 0 0 2 2 0 2 0 2 0 0 0 0 0 0 0 2 2 0 0 2 2 2 0 2 0 2 2 2 0 0 2 0 2 2 0 2 2 2 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 0 0 2 0 2 2 2 0 2 0 2 2 2 0 2 2 0 2 0 0 2 0 2 2 2 0 0 0 2 0 0 0 0 2 0 2 2 2 0 2 0 2 0 2 0 2 0 0 0 2 2 2 2 2 2 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 0 0 0 0 2 0 0 0 0 2 2 0 0 2 2 0 2 0 2 0 0 2 0 0 2 2 2 0 0 0 2 0 2 2 2 0 2 0 2 0 2 0 0 2 2 2 0 0 2 0 0 2 0 0 2 0 2 0 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 0 2 2 2 2 0 2 0 2 2 2 0 2 0 2 0 2 0 0 2 2 2 0 2 2 0 0 2 2 2 0 2 2 0 0 2 2 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 2 2 0 0 2 generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+116x^68+4x^70+215x^72+82x^74+308x^76+680x^78+1369x^80+692x^82+243x^84+68x^86+154x^88+10x^90+90x^92+47x^96+11x^100+5x^104+1x^128 The gray image is a code over GF(2) with n=320, k=12 and d=136. This code was found by Heurico 1.16 in 2.6 seconds.