The generator matrix

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

generates a code of length 14 over F4[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+192x^34+114x^36+576x^38+387x^40+1344x^42+468x^44+960x^46+3x^48+42x^52+9x^56

The gray image is a linear code over GF(4) with n=56, k=6 and d=34.
This code was found by Heurico 1.16 in 0.936 seconds.