The generator matrix

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

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+108x^28+240x^29+204x^30+1020x^31+708x^32+1620x^33+1932x^34+3420x^35+3657x^36+5460x^37+5892x^38+10068x^39+8730x^40+8604x^41+5796x^42+5460x^43+1602x^44+972x^45+33x^48+9x^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 1.94 seconds.