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

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+660x^107+510x^108+96x^109+492x^110+1404x^111+1020x^112+180x^113+588x^114+2136x^115+1176x^116+228x^117+468x^118+2040x^119+1242x^120+156x^121+516x^122+1716x^123+726x^124+108x^125+240x^126+492x^127+174x^128+12x^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 243 seconds.