The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  1  1  1  0 aX  1  1  1  1  1  1 aX  1  1  0  X
 0  1  0  0  1  X (a+1)X+1  1  a X+a a+1 X+a+1 aX  1  1  X a+1 (a+1)X+a (a+1)X+a (a+1)X+a+1 (a+1)X+a aX  X X+1 (a+1)X+a+1  1  0
 0  0  1  0 a+1 (a+1)X+1  a (a+1)X+1  0 aX+1  1 (a+1)X (a+1)X (a+1)X+1 (a+1)X+a  1 X+a (a+1)X+1  X (a+1)X+a+1 X+a+1  0  1  a (a+1)X aX+a  1
 0  0  0  1  1 a+1  a aX+a+1  a X+1 aX+a (a+1)X+1 X+1 X+a+1 aX+a a+1 (a+1)X+a+1 (a+1)X+a+1 X+a+1  X X+a X+a (a+1)X (a+1)X+1  1 X+1 (a+1)X+a
 0  0  0  0 (a+1)X  0 (a+1)X  0  X  X  X  X (a+1)X aX  X (a+1)X aX (a+1)X  0 aX (a+1)X  X aX  0  0 aX  0

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

Homogenous weight enumerator: w(x)=1x^0+324x^66+540x^67+987x^68+924x^69+2520x^70+2052x^71+4626x^72+3888x^73+8616x^74+5952x^75+12150x^76+9912x^77+20544x^78+14136x^79+25836x^80+16800x^81+31716x^82+17676x^83+24891x^84+14796x^85+19464x^86+7812x^87+9180x^88+2832x^89+2832x^90+984x^91+63x^92+63x^96+18x^100+6x^104+3x^108

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 77 seconds.