The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+405x^68+288x^69+60x^70+1056x^71+1698x^72+1128x^73+240x^74+2448x^75+4317x^76+3168x^77+840x^78+6480x^79+7623x^80+5424x^81+1200x^82+7728x^83+8070x^84+4416x^85+732x^86+3792x^87+3306x^88+936x^89+93x^92+54x^96+27x^100+6x^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 6.55 seconds.