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 2 X 0 X 1 2 1 X X 1 1 2 1 2 1 2 1 1 2 0 1 1 1 X X 1 1 0 X X 1 X 1 1 1 X X 1 1 X 1 2 X 1 1 1 1 X 2 1 0 X 0 0 0 0 0 0 2 2 X X+2 X 0 0 2 X+2 X+2 X X X X 0 X X+2 X 0 X X+2 2 X+2 2 2 X+2 X 0 0 X 2 X X 0 X+2 X 2 X+2 2 X+2 X 2 X 2 X X+2 0 X+2 X X X 0 2 X 2 0 0 X X X+2 X+2 2 X+2 2 0 0 0 0 X+2 X 2 X 2 2 X 0 2 2 X 2 2 0 0 X 0 0 0 0 0 0 0 0 0 2 X+2 X+2 X+2 X X+2 X+2 X 2 2 X+2 X+2 0 0 X X X X+2 X+2 X+2 2 2 X+2 X X 2 2 X+2 0 2 X 0 X 2 0 2 X 2 X+2 0 X+2 X+2 0 0 0 X+2 2 X+2 0 X 2 X 0 0 X 2 0 X+2 2 2 X+2 X 2 X+2 0 X 2 2 2 X 2 X 2 X X X 0 0 0 0 X 0 0 2 X+2 X X X X 2 X+2 X 2 2 0 2 2 2 2 2 X X+2 X 2 X X+2 X+2 X X+2 0 2 0 0 0 X+2 X+2 X X+2 X X+2 2 2 2 X X 0 X+2 0 X+2 X X+2 X X+2 2 X+2 X 2 2 X X X+2 2 2 X X X X X 0 0 X X 0 2 0 2 X X 0 X+2 X 2 X X+2 0 X+2 0 0 0 0 X 0 X+2 X+2 X 2 X+2 X+2 0 X X 0 2 X 0 X+2 X+2 X X+2 X 2 2 X 2 2 0 X+2 2 0 X+2 X X+2 2 0 X+2 X+2 X X+2 X+2 2 2 X+2 2 0 0 0 2 0 0 2 X+2 X+2 2 0 X X X X X+2 X+2 0 2 X+2 0 2 X 2 0 0 X+2 0 2 X 0 2 2 2 X+2 X+2 X+2 0 0 X+2 0 X+2 0 0 0 0 0 X X 2 X+2 X X+2 2 X X 0 X 0 X+2 X+2 0 X 2 2 X+2 2 X X+2 X+2 2 X 2 2 X+2 0 X X+2 0 0 0 0 X X X+2 0 X+2 X+2 0 2 X+2 0 0 X+2 X 2 2 X+2 X+2 2 2 X X+2 2 X+2 2 2 2 0 X 2 0 X+2 0 2 X X+2 2 X+2 X X 0 2 X+2 2 X+2 X X 0 X+2 2 generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+51x^78+126x^79+181x^80+262x^81+244x^82+350x^83+392x^84+470x^85+547x^86+610x^87+727x^88+632x^89+664x^90+560x^91+489x^92+402x^93+312x^94+268x^95+210x^96+192x^97+123x^98+92x^99+67x^100+72x^101+38x^102+36x^103+36x^104+18x^105+5x^106+6x^107+8x^108+1x^128 The gray image is a code over GF(2) with n=356, k=13 and d=156. This code was found by Heurico 1.16 in 8.54 seconds.