The generator matrix

 1  0  1  1  1  1  1  1  1  1
 0  1  1  a a^2*X+a^2  0 a^2*X+1 a^2*X+a^2  X  X
 0  0 a^2*X a*X  X  X  0 a^2*X a*X a^2*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+33x^24+72x^26+96x^27+165x^28+48x^30+288x^31+234x^32+72x^34+15x^36

The gray image is a linear code over GF(4) with n=40, k=5 and d=24.
This code was found by Heurico 1.16 in 1.01e-007 seconds.