The generator matrix

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

generates a code of length 11 over F4[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+15x^28+24x^32+192x^33+15x^36+3x^40+6x^44

The gray image is a linear code over GF(4) with n=44, k=4 and d=28.
This code was found by Heurico 1.16 in 6.87e-008 seconds.