The generator matrix 1 0 0 1 1 1 X 1 1 X+2 1 1 X X+2 X X+2 1 1 0 1 1 X+2 1 1 1 1 2 2 1 0 0 1 2 1 1 1 1 1 0 1 1 2 2 1 1 X+2 1 X+2 0 1 X+2 X+2 1 1 X 0 1 1 1 1 1 1 1 1 1 X+2 1 1 1 2 X 1 X+2 1 0 1 0 2 2 0 0 X+2 1 X+2 1 1 1 0 1 0 X 1 X+3 1 X+2 0 2 1 X+1 X+2 1 1 1 X 3 1 0 X+1 1 X+2 0 X+1 1 1 X 2 1 1 X 0 X+1 X+3 2 X+2 3 1 3 X+2 X 2 2 2 1 X+3 X+2 1 3 1 X 0 X+2 X+2 1 3 3 2 X 0 X+1 X+3 0 1 2 0 1 1 X+2 1 2 2 2 1 0 1 1 1 1 1 1 X+1 1 X+2 3 X+3 0 0 1 1 X+3 X+2 1 X+3 X+2 1 1 0 1 X+1 X 0 X+2 2 1 X+3 3 X+2 0 3 X+3 X 1 1 X X+2 X+1 X+2 1 X+2 X+1 X+2 X+3 1 X+1 X 1 1 1 0 X+2 0 3 1 3 0 3 1 X+3 X+1 1 X X+1 X+2 X+3 X+3 X+3 2 X+1 3 1 1 0 2 3 1 X+3 X+2 1 X+2 3 2 X X 2 X+1 X+3 2 3 X+3 3 X X 0 0 0 2 0 0 0 0 2 2 0 0 0 2 2 0 2 0 2 2 2 2 2 2 0 2 0 2 2 2 0 0 2 0 2 0 0 0 0 2 0 0 0 0 0 2 0 2 2 2 2 0 0 0 2 2 0 2 0 0 2 2 0 2 0 0 2 0 0 2 0 2 0 0 2 0 2 0 0 0 2 2 2 2 2 2 2 0 0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 2 2 0 0 2 0 0 0 2 2 0 2 0 0 2 2 0 2 2 0 0 2 0 2 0 0 2 2 0 2 2 0 0 0 2 2 0 2 2 0 0 2 0 2 2 0 2 2 0 0 0 2 2 0 2 2 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 2 2 2 0 2 2 2 2 2 2 2 0 2 0 2 2 2 0 2 0 2 2 0 2 0 2 0 0 2 0 0 2 0 0 2 2 2 2 2 0 0 2 0 0 0 2 2 0 2 0 2 2 2 0 0 0 2 2 0 2 2 2 0 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 2 2 2 2 2 2 0 0 0 0 2 0 0 0 2 2 0 0 0 0 2 2 2 2 0 2 2 0 2 0 0 2 2 0 2 2 2 2 0 2 2 2 0 0 0 0 0 0 2 0 2 2 0 0 2 0 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 0 0 2 0 0 0 0 0 2 2 2 2 2 0 2 0 0 0 2 0 2 0 2 0 2 2 0 2 2 2 0 2 2 0 0 0 0 2 2 2 0 0 0 0 0 2 2 0 0 0 2 2 2 0 0 0 2 2 0 2 2 2 2 0 0 2 2 2 2 0 0 0 2 2 generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77. Homogenous weight enumerator: w(x)=1x^0+80x^77+205x^78+470x^79+405x^80+958x^81+640x^82+1240x^83+956x^84+1650x^85+960x^86+1734x^87+956x^88+1472x^89+813x^90+1192x^91+562x^92+772x^93+357x^94+410x^95+154x^96+158x^97+76x^98+64x^99+34x^100+26x^101+13x^102+10x^103+4x^104+4x^105+7x^106+1x^118 The gray image is a code over GF(2) with n=348, k=14 and d=154. This code was found by Heurico 1.16 in 36.9 seconds.