The generator matrix

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

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+588x^72+480x^74+1044x^76+288x^78+549x^80+288x^82+756x^84+96x^86+6x^88

The gray image is a linear code over GF(4) with n=104, k=6 and d=72.
This code was found by Heurico 1.16 in 0.047 seconds.