The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1  1
 0  1  0 a^2*X a*X a^2*X+1  a  1 X+1  X a*X+1 a*X+a^2 a^2*X+a^2 X+a^2
 0  0  1  1  a X+a a^2*X+a X+1 a^2*X+a^2 a^2 a^2*X a*X+a X+a^2  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+57x^36+324x^37+360x^38+360x^39+303x^40+648x^41+240x^42+459x^44+756x^45+360x^46+216x^47+12x^48

The gray image is a linear code over GF(4) with n=56, k=6 and d=36.
This code was found by Heurico 1.16 in 0.016 seconds.