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 0 X X 1 1 2 1 1 2 1 X 1 1 1 2 1 1 2 1 X 1 2 1 1 1 1 0 X 1 1 1 2 X 1 1 2 X 1 1 2 1 1 1 1 0 X 0 0 0 X X+2 X 0 2 2 0 X X+2 X X+2 X+2 X+2 X+2 2 0 0 X+2 2 0 2 X X X+2 2 X+2 X X+2 2 2 0 0 0 X+2 X+2 0 2 2 X 0 2 X X+2 X 2 X 0 2 X X+2 0 X 0 0 X+2 0 X X+2 2 2 2 X X X+2 X X+2 X X+2 2 X X+2 X 0 2 X 2 0 0 X+2 2 X+2 0 0 0 X 0 X X X+2 0 0 0 X+2 X+2 X X 2 0 X 2 0 X+2 X+2 2 X+2 2 X+2 0 2 2 X+2 X+2 0 X+2 0 2 0 X+2 2 X X+2 X 0 2 X X+2 2 X X+2 X+2 2 2 2 X 0 0 X+2 X+2 2 0 2 X+2 2 X+2 X+2 X X X 0 X 2 X+2 X X+2 X+2 X 0 2 2 X+2 X X X X+2 X 2 X 2 X+2 0 0 0 X X 0 X+2 X 2 X+2 X 2 2 X X 2 0 X+2 0 X 2 X X 0 2 X 0 X+2 X X X+2 2 X+2 0 0 X X+2 X 0 0 X 0 X+2 X X 2 0 X X X+2 X X+2 2 X X+2 2 0 X 2 2 X X+2 X X X X+2 2 2 0 2 0 X+2 0 2 0 2 X X 2 X+2 X+2 2 0 2 2 X X+2 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 0 2 2 0 2 0 2 2 0 0 0 2 2 0 0 0 2 2 0 2 2 2 2 2 2 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 2 0 2 2 0 0 2 0 0 2 2 0 0 2 2 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 0 2 2 0 0 0 2 2 2 0 0 2 2 2 0 0 0 0 0 2 2 0 2 2 0 0 2 2 2 2 2 0 2 2 0 2 2 2 0 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 0 0 0 2 2 0 0 2 0 0 2 2 2 0 0 2 0 2 0 0 0 0 0 0 0 0 2 2 2 2 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 2 2 2 0 0 0 2 0 2 0 2 2 2 2 0 2 2 2 0 2 2 0 2 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 2 2 0 2 2 0 2 0 0 2 0 0 2 0 0 2 2 generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78. Homogenous weight enumerator: w(x)=1x^0+142x^78+243x^80+44x^81+362x^82+112x^83+423x^84+236x^85+461x^86+256x^87+482x^88+196x^89+329x^90+144x^91+211x^92+36x^93+146x^94+114x^96+74x^98+53x^100+19x^102+8x^104+3x^106+1x^140 The gray image is a code over GF(2) with n=348, k=12 and d=156. This code was found by Heurico 1.16 in 2.34 seconds.