The generator matrix

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

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+486x^24+576x^25+1056x^26+768x^27+2844x^28+1728x^29+4320x^30+4608x^31+9807x^32+7104x^33+11232x^34+6912x^35+9336x^36+2880x^37+1824x^38+42x^40+12x^44

The gray image is a linear code over GF(4) with n=44, k=8 and d=24.
This code was found by Heurico 1.16 in 2.29 seconds.