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.