The generator matrix

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

generates a code of length 27 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+180x^64+12x^66+180x^67+342x^68+48x^69+180x^70+1212x^71+516x^72+576x^73+1080x^74+4872x^75+531x^76+2592x^77+3240x^78+10872x^79+576x^80+5184x^81+4860x^82+13188x^83+609x^84+3888x^85+2916x^86+6540x^87+600x^88+477x^92+207x^96+57x^100

The gray image is a linear code over GF(4) with n=108, k=8 and d=64.
This code was found by Heurico 1.16 in 7.19 seconds.