The generator matrix

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

generates a code of length 13 over F4[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+432x^34+504x^35+69x^36+864x^38+528x^39+180x^40+1008x^42+504x^43+3x^48+3x^52

The gray image is a linear code over GF(4) with n=52, k=6 and d=34.
This code was found by Heurico 1.16 in 0.031 seconds.