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 X 0 X 0 1 X 1 0 X 1 1 1 0 1 X 0 1 0 1 1 1 X 1 1 X X 1 0 X 0 X 1 1 0 X 0 X+2 0 X+2 0 X+2 0 X+2 2 X+2 0 X+2 0 X+2 X 2 X+2 0 2 X+2 2 X+2 X X+2 X X+2 X+2 X+2 X X+2 0 0 X X 0 X+2 X 0 X X+2 X X X+2 X+2 0 X+2 2 2 X 0 X X+2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 2 2 2 2 2 0 0 0 2 0 2 2 2 2 0 0 0 0 2 2 2 0 2 0 0 0 0 2 2 0 0 0 0 2 0 2 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 2 0 2 0 0 2 0 2 2 0 0 2 2 2 0 0 2 2 2 0 0 0 0 2 2 2 0 0 2 0 0 2 2 2 2 2 2 2 2 2 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2 2 0 0 2 2 2 0 2 2 2 2 0 0 2 0 2 2 0 2 2 2 2 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 2 2 2 2 2 0 2 0 2 0 2 2 2 2 2 0 0 2 0 2 0 0 0 2 0 2 2 2 0 2 0 2 2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 2 0 0 0 0 2 2 0 2 2 0 2 0 0 2 2 0 2 2 0 2 2 2 0 0 0 2 0 0 2 2 2 2 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 2 2 0 2 2 0 2 2 0 2 0 2 0 0 2 2 0 2 0 0 2 0 0 0 2 2 0 0 0 2 0 2 0 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 2 2 0 2 0 2 0 0 2 0 0 2 2 2 2 2 0 0 2 0 2 2 0 2 0 2 0 0 0 0 0 2 2 2 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 0 2 2 2 2 0 0 2 2 2 2 0 2 2 0 2 0 0 2 2 0 0 2 0 0 2 0 2 0 0 2 0 0 0 0 0 0 2 2 0 0 generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 44. Homogenous weight enumerator: w(x)=1x^0+83x^44+62x^46+319x^48+358x^50+1010x^52+1376x^54+1829x^56+1356x^58+986x^60+382x^62+256x^64+46x^66+90x^68+4x^70+27x^72+7x^76 The gray image is a code over GF(2) with n=224, k=13 and d=88. This code was found by Heurico 1.16 in 4.91 seconds.