The generator matrix

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

generates a code of length 14 over F4[X]/(X^2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+96x^33+528x^34+114x^36+864x^37+1584x^38+387x^40+2592x^41+4464x^42+468x^44+2592x^45+2640x^46+3x^48+42x^52+9x^56

The gray image is a linear code over GF(4) with n=56, k=7 and d=33.
This code was found by Heurico 1.16 in 0.125 seconds.