The generator matrix

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

generates a code of length 27 over F4[X]/(X^2) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+336x^66+420x^67+819x^68+996x^69+3288x^70+1872x^71+3711x^72+3780x^73+9948x^74+5832x^75+10617x^76+9816x^77+23520x^78+14784x^79+21489x^80+17016x^81+34584x^82+17748x^83+21189x^84+14724x^85+23208x^86+7824x^87+7539x^88+2820x^89+3420x^90+672x^91+87x^92+54x^96+24x^100+6x^104

The gray image is a linear code over GF(4) with n=108, k=9 and d=66.
This code was found by Heurico 1.16 in 78.6 seconds.