The generator matrix

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

generates a code of length 11 over F4[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+30x^24+66x^28+39x^32+768x^33+60x^36+42x^40+18x^44

The gray image is a linear code over GF(4) with n=44, k=5 and d=24.
This code was found by Heurico 1.16 in -6.87e-008 seconds.