The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  X  X  X a*X a*X a^2*X  0  0  X a*X a*X  X  X  0  X a*X a*X  0  0  X
 0  0  X  0  0  X a^2*X a^2*X a*X  0 a^2*X  0 a*X  X  X a^2*X a*X  0 a*X a^2*X a^2*X  0  0  X a*X a^2*X
 0  0  0  X  0 a^2*X  0 a^2*X  X a*X a^2*X a*X a^2*X a^2*X a^2*X  0 a*X a*X  X  0  0 a^2*X  0  X a^2*X  X
 0  0  0  0  X  X  X a^2*X a^2*X a^2*X a*X  X a^2*X a^2*X a^2*X a^2*X a*X  0  0  X a*X  X  X a^2*X a*X a^2*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+48x^64+159x^68+162x^72+174x^76+3072x^78+150x^80+135x^84+105x^88+48x^92+27x^96+12x^100+3x^104

The gray image is a linear code over GF(4) with n=104, k=6 and d=64.
This code was found by Heurico 1.16 in 0.0621 seconds.