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

generates a code of length 26 over F4[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+93x^72+192x^75+72x^76+576x^79+27x^80+21x^84+15x^88+18x^92+9x^100

The gray image is a linear code over GF(4) with n=104, k=5 and d=72.
This code was found by Heurico 1.16 in 0.031 seconds.