The generator matrix

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

generates a code of length 24 over F4[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+147x^68+192x^69+144x^70+159x^72+96x^73+129x^76+96x^77+48x^78+9x^80+3x^96

The gray image is a linear code over GF(4) with n=96, k=5 and d=68.
This code was found by Heurico 1.16 in 1.01e-007 seconds.