The generator matrix

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

generates a code of length 13 over F4[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+81x^24+324x^28+576x^30+456x^32+1536x^33+5184x^34+750x^36+9216x^37+15552x^38+1143x^40+13824x^41+15552x^42+840x^44+399x^48+102x^52

The gray image is a linear code over GF(4) with n=52, k=8 and d=24.
This code was found by Heurico 1.16 in 1.7 seconds.