The generator matrix

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

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+732x^107+399x^108+2352x^111+957x^112+3072x^115+987x^116+3048x^119+948x^120+2340x^123+573x^124+744x^127+219x^128+9x^132+3x^144

The gray image is a linear code over GF(4) with n=156, k=7 and d=107.
This code was found by Heurico 1.16 in 8.27 seconds.