The generator matrix

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

generates a code of length 14 over F4[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+147x^32+348x^36+1350x^40+1896x^44+276x^48+60x^52+18x^56

The gray image is a linear code over GF(4) with n=56, k=6 and d=32.
This code was found by Heurico 1.16 in 0.211 seconds.