The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 1 1
0 X 0 0 0 0 0 X X a*X X X 0 X
0 0 X 0 0 0 X a^2*X a^2*X 0 a*X a*X 0 X
0 0 0 X 0 0 a^2*X X 0 a*X a^2*X a*X a*X 0
0 0 0 0 X 0 X a^2*X a*X a^2*X 0 X X a^2*X
0 0 0 0 0 X a^2*X X a^2*X a^2*X a*X a^2*X X a^2*X
generates a code of length 14 over F4[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+168x^28+387x^32+1284x^36+5358x^40+8064x^44+756x^48+276x^52+90x^56
The gray image is a linear code over GF(4) with n=56, k=7 and d=28.
This code was found by Heurico 1.16 in 0.291 seconds.