The generator matrix

 1  0  0  1  1  1 a^2*X  1  1  1  1
 0  1  0  1  a a^2  1 a^2*X a^2*X+1 a^2*X  0
 0  0  1 a^2  a  1  1  1  0 X+a^2  X
 0  0  0  X  0  X a^2*X a*X a*X a^2*X a^2*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+126x^24+144x^25+108x^26+192x^27+1035x^28+432x^29+732x^30+1152x^31+2991x^32+1776x^33+2052x^34+1728x^35+2958x^36+720x^37+180x^38+42x^40+15x^44

The gray image is a linear code over GF(4) with n=44, k=7 and d=24.
This code was found by Heurico 1.16 in 0.094 seconds.