The generator matrix

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

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+1608x^112+864x^116+864x^120+480x^124+279x^128

The gray image is a linear code over GF(4) with n=156, k=6 and d=112.
This code was found by Heurico 1.16 in 65 seconds.