The generator matrix

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

generates a code of length 26 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+144x^68+336x^69+96x^70+480x^71+1203x^72+1152x^73+180x^74+960x^75+1704x^76+1584x^77+228x^78+1440x^79+2055x^80+1440x^81+156x^82+960x^83+1248x^84+864x^85+108x^86+21x^88+24x^92

The gray image is a linear code over GF(4) with n=104, k=7 and d=68.
This code was found by Heurico 1.16 in 0.392 seconds.