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.