The generator matrix

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

generates a code of length 11 over F4[X]/(X^2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+96x^31+39x^32+96x^35+24x^36

The gray image is a linear code over GF(4) with n=44, k=4 and d=31.
This code was found by Heurico 1.16 in -6.87e-008 seconds.