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  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  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  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  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  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  0

generates a code of length 28 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+75x^64+36x^67+219x^68+12x^69+132x^70+300x^71+441x^72+180x^73+780x^74+984x^75+1134x^76+1080x^77+3240x^78+1944x^79+3042x^80+3240x^81+7320x^82+3156x^83+5760x^84+4860x^85+8724x^86+3708x^87+4476x^88+2916x^89+4380x^90+2160x^91+570x^92+426x^96+189x^100+51x^104

The gray image is a linear code over GF(4) with n=112, k=8 and d=64.
This code was found by Heurico 1.16 in 7.2 seconds.