The generator matrix

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

generates a code of length 14 over F4[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+66x^36+99x^40+768x^42+36x^44+3x^48+42x^52+9x^56

The gray image is a linear code over GF(4) with n=56, k=5 and d=36.
This code was found by Heurico 1.16 in 0.062 seconds.