The generator matrix

 1  0  0  1  1  1  1  1  1  1 a^2*X  1 a^2*X  1  1  1  1  1  1  0  1  1  1 a*X  1  1
 0  1  0  0  X a^2*X  1 a^2*X+a a^2  1  1 a^2*X+a^2  1  a a^2*X+1 a^2 X+a a^2*X+1 X+a  1 a*X+a^2 a^2*X+a^2 a^2*X+a  1  0 a^2*X
 0  0  1  1 a^2*X+a a^2 a^2 X+a^2 X+a^2 X+1 X+a^2 a*X X+1  a X+a X+1 a*X+1  0  X X+a a^2*X+a X+a a^2*X+a^2  0 a^2*X+a^2 a*X+1
 0  0  0 a^2*X a*X a*X  X  X a^2*X a^2*X  X  0  0 a*X  0  0  X a^2*X a*X a^2*X  X a*X a^2*X a*X  X a*X

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

Homogenous weight enumerator: w(x)=1x^0+195x^68+204x^69+180x^70+384x^71+1608x^72+660x^73+408x^74+768x^75+2346x^76+828x^77+384x^78+1152x^79+2805x^80+924x^81+360x^82+768x^83+1707x^84+456x^85+204x^86+18x^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 0.393 seconds.