The generator matrix

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

generates a code of length 37 over F4[X]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+225x^100+156x^101+144x^102+408x^103+1437x^104+684x^105+348x^106+804x^107+2004x^108+756x^109+360x^110+720x^111+2370x^112+660x^113+384x^114+696x^115+1980x^116+576x^117+264x^118+408x^119+660x^120+240x^121+36x^122+36x^123+12x^124+9x^128+3x^132+3x^136

The gray image is a linear code over GF(4) with n=148, k=7 and d=100.
This code was found by Heurico 1.16 in 0.485 seconds.