The generator matrix

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

generates a code of length 13 over F4[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+339x^28+144x^29+288x^30+1548x^32+1728x^33+2592x^34+5640x^36+8928x^37+7776x^38+11022x^40+13248x^41+7776x^42+3843x^44+528x^45+117x^48+18x^52

The gray image is a linear code over GF(4) with n=52, k=8 and d=28.
This code was found by Heurico 1.16 in 13.5 seconds.