The generator matrix

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

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+414x^100+564x^101+180x^102+1368x^103+2448x^104+2712x^105+1332x^106+4224x^107+7080x^108+6996x^109+2772x^110+10080x^111+14781x^112+14148x^113+5592x^114+18528x^115+24048x^116+20748x^117+6972x^118+22776x^119+25251x^120+19536x^121+5796x^122+13536x^123+13254x^124+8076x^125+1884x^126+3216x^127+2712x^128+948x^129+48x^130+69x^132+24x^136+12x^140+12x^144+3x^148+3x^152

The gray image is a linear code over GF(4) with n=156, k=9 and d=100.
This code was found by Heurico 1.16 in 127 seconds.