The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0
 0  1  1  a a^2  0 a^2*X+1  a a^2*X+a^2  1  0 a^2*X+1  a  1
 0  0 a^2*X  0  0  X  0 a*X a*X a*X  X  X  X  0
 0  0  0  X  0 a^2*X a*X a^2*X a^2*X  0 a^2*X  0  X a*X
 0  0  0  0 a^2*X  X  X a^2*X  0  0 a*X  X  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+192x^33+348x^36+1728x^37+1350x^40+5184x^41+1896x^44+5184x^45+276x^48+60x^52+18x^56

The gray image is a linear code over GF(4) with n=56, k=7 and d=32.
This code was found by Heurico 1.16 in 2.38 seconds.