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.