The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1 a^2*X  0 a*X  1  1 a*X  1 a*X  1
 0  1  0  0  0 a^2*X  1 a^2*X+a a^2  1 a^2*X+1 a^2*X+a^2 a^2  a  a  1 a*X+a a^2*X+1  1  1  1 a^2*X+a  X a*X a^2*X+a^2  1  0
 0  0  1  1  a a^2  1 X+1  1 a^2  0  a a^2  0 X+a  1 a*X+a^2  a a*X+a^2 a*X+1  a a^2*X+a a*X+a^2  1 X+1 a*X  X
 0  0  0 a^2*X  0  0  0  X  X  X a*X a*X a^2*X a*X a^2*X a*X a*X a*X a^2*X a^2*X  X  0 a*X  X  0  0 a^2*X
 0  0  0  0  X a^2*X a*X  X a^2*X a*X a*X a^2*X a*X  X a*X a*X a^2*X  0  0 a^2*X  0  0  0 a*X  0 a^2*X a*X

generates a code of length 27 over F4[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+297x^68+312x^69+168x^70+1068x^71+1359x^72+1476x^73+768x^74+2448x^75+3381x^76+2832x^77+2448x^78+6408x^79+5505x^80+5256x^81+3648x^82+7824x^83+6234x^84+4248x^85+2184x^86+3756x^87+2514x^88+1236x^89+93x^92+36x^96+27x^100+9x^104

The gray image is a linear code over GF(4) with n=108, k=8 and d=68.
This code was found by Heurico 1.16 in 6.39 seconds.