The generator matrix
1 0 1 1 1 1 1 1 1 1 1 1 0
0 1 1 a a^2*X+a^2 0 a^2*X+1 0 X X a a^2*X+a^2 1
0 0 a^2*X 0 X 0 X a^2*X a^2*X a*X a*X X 0
0 0 0 X a*X a*X 0 X a^2*X a^2*X a*X a^2*X X
generates a code of length 13 over F4[X]/(X^2) who´s minimum homogenous weight is 32.
Homogenous weight enumerator: w(x)=1x^0+168x^32+192x^33+222x^36+1152x^37+366x^40+1728x^41+228x^44+33x^48+6x^52
The gray image is a linear code over GF(4) with n=52, k=6 and d=32.
This code was found by Heurico 1.16 in 0.0121 seconds.