The generator matrix

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

generates a code of length 27 over F4[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+456x^69+696x^70+444x^71+969x^72+1848x^73+2388x^74+1020x^75+2667x^76+4308x^77+4572x^78+2628x^79+4398x^80+7044x^81+6756x^82+3732x^83+5349x^84+6324x^85+4668x^86+1392x^87+1425x^88+1524x^89+888x^90+21x^92+15x^96+3x^100

The gray image is a linear code over GF(4) with n=108, k=8 and d=69.
This code was found by Heurico 1.16 in 6.02 seconds.