The generator matrix

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

generates a code of length 11 over F4[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+192x^21+780x^22+885x^24+2304x^25+3120x^26+3840x^27+6645x^28+10368x^29+23976x^30+23040x^31+19605x^32+33024x^33+54768x^34+34560x^35+19770x^36+15552x^37+9516x^38+165x^40+33x^44

The gray image is a linear code over GF(4) with n=44, k=9 and d=21.
This code was found by Heurico 1.16 in 15.4 seconds.