The generator matrix

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

generates a code of length 10 over F4[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+315x^24+1500x^28+2205x^32+60x^36+15x^40

The gray image is a linear code over GF(4) with n=40, k=6 and d=24.
This code was found by Heurico 1.16 in 0.00711 seconds.