The generator matrix

 1  0  1  1  1  1  1  1  1  0  1
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1  a
 0  0 a^2*X  0  0  X  0 a*X a*X  X a*X
 0  0  0  X  0 a^2*X a*X a^2*X  X  X a^2*X
 0  0  0  0 a^2*X  X  X a^2*X a^2*X  X  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+213x^24+768x^27+597x^28+4608x^31+1461x^32+6912x^35+1626x^36+165x^40+33x^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 0.108 seconds.