The generator matrix

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

generates a code of length 26 over F4[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+138x^64+108x^65+324x^67+1824x^68+876x^69+1176x^71+4998x^72+2040x^73+3144x^75+12291x^76+3672x^77+4464x^79+14202x^80+3996x^81+2964x^83+7293x^84+1596x^85+216x^87+102x^88+93x^92+15x^96+3x^100

The gray image is a linear code over GF(4) with n=104, k=8 and d=64.
This code was found by Heurico 1.16 in 5.91 seconds.