The generator matrix

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

generates a code of length 11 over F4[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+84x^27+300x^28+288x^29+48x^30+504x^31+600x^32+384x^33+144x^34+756x^35+693x^36+288x^37+3x^40+3x^44

The gray image is a linear code over GF(4) with n=44, k=6 and d=27.
This code was found by Heurico 1.16 in -3.24e-008 seconds.