The generator matrix 1 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 a a^2 0 a^2*X+1 a a^2*X+a^2 1 1 a^2*X+1 a a^2*X+a^2 0 a^2*X+a^2 1 a^2*X+1 a^2*X+a^2 a^2*X+1 a a*X+1 X+a a^2*X+1 a 1 a^2*X+1 0 0 a^2*X 0 0 0 0 X a*X X a*X a*X 0 X 0 a*X a*X a^2*X X X X a*X a^2*X a*X 0 0 X 0 0 0 X 0 0 X a^2*X a^2*X a*X 0 X X 0 X a^2*X X a*X a^2*X X X 0 a^2*X X a^2*X X 0 0 0 0 0 a^2*X 0 a*X 0 X X a*X a^2*X a*X a^2*X X 0 a*X a^2*X 0 a^2*X a^2*X X a^2*X X a^2*X a^2*X a*X 0 0 0 0 0 X a*X X a*X a*X X a^2*X X a^2*X 0 a^2*X 0 a^2*X a*X 0 a^2*X 0 X 0 X a^2*X a*X generates a code of length 27 over F4[X]/(X^2) who´s minimum homogenous weight is 64. Homogenous weight enumerator: w(x)=1x^0+171x^64+48x^65+24x^66+60x^67+411x^68+324x^69+360x^70+420x^71+603x^72+972x^73+2160x^74+1560x^75+2250x^76+2664x^77+6480x^78+3720x^79+5829x^80+3720x^81+9720x^82+4332x^83+5802x^84+3348x^85+5832x^86+2196x^87+621x^88+1212x^89+402x^92+231x^96+63x^100 The gray image is a linear code over GF(4) with n=108, k=8 and d=64. This code was found by Heurico 1.16 in 7.49 seconds.