The generator matrix 1 0 0 0 1 1 1 0 1 1 1 1 X X X X 0 1 0 1 X 1 1 1 1 X 1 1 X 0 X 1 1 1 1 0 0 1 0 1 X 0 0 X 0 1 1 0 0 1 1 X X 1 0 1 0 0 0 1 1 1 0 0 1 X+1 1 0 1 1 X X 0 X+1 1 X 1 1 X+1 1 X X 0 1 X 1 X+1 0 X 1 1 X 1 1 X 1 1 0 1 X 1 X X 0 X X X 0 0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 X 1 0 X 0 1 X+1 1 X+1 0 X X+1 0 1 1 1 X+1 X 1 1 X+1 X X 1 1 1 X+1 X+1 X X 0 0 1 X 1 0 0 0 0 0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 X X 1 1 X X+1 1 X X+1 1 1 X X 1 X+1 0 1 1 0 1 X X+1 X+1 1 X X+1 X X 1 X+1 0 X X 1 0 X+1 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X X X X 0 X 0 X 0 X X X 0 0 X 0 X X 0 0 0 X X X 0 X X X X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X X X 0 0 0 0 X 0 X 0 X X 0 0 X X 0 0 X 0 X X 0 X 0 0 X X 0 0 X 0 0 0 X X 0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X 0 0 X X 0 X X 0 X 0 0 0 X X 0 X 0 X 0 0 0 0 0 X X 0 X 0 0 X X X 0 X 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 0 X X X X 0 X 0 0 0 X 0 X 0 0 X X 0 X X X X X 0 0 X 0 0 X 0 0 X 0 0 X 0 X 0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 X X X X X X X 0 0 X 0 X X 0 X 0 X X 0 0 X 0 X X 0 0 0 X 0 X 0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 0 X X X 0 X 0 X X 0 X X X 0 0 X 0 X X 0 0 X X X X 0 X X X 0 X 0 X 0 X X X 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X X X X X X X 0 0 X X X 0 0 X X X 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 40. Homogenous weight enumerator: w(x)=1x^0+91x^40+90x^41+250x^42+298x^43+492x^44+672x^45+880x^46+1058x^47+1319x^48+1430x^49+1716x^50+2088x^51+2138x^52+2496x^53+2426x^54+2448x^55+2325x^56+2198x^57+1882x^58+1674x^59+1266x^60+1056x^61+820x^62+514x^63+436x^64+218x^65+176x^66+100x^67+102x^68+32x^69+34x^70+12x^71+20x^72+8x^74+2x^76 The gray image is a linear code over GF(2) with n=108, k=15 and d=40. This code was found by Heurico 1.16 in 99.9 seconds.