The generator matrix

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

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+36x^116+192x^117+12x^120+12x^124+3x^128

The gray image is a linear code over GF(4) with n=156, k=4 and d=116.
As d=116 is an upper bound for linear (156,4,4)-codes, this code is optimal over F4[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 6.87e-008 seconds.