The generator matrix

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

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+78x^24+324x^25+144x^26+144x^27+459x^28+648x^29+288x^30+432x^31+666x^32+756x^33+144x^34+9x^36+3x^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 -1.01e-007 seconds.