The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+87x^100+72x^101+324x^103+330x^104+408x^105+840x^107+462x^108+1008x^109+1224x^111+1176x^112+1872x^113+1872x^115+1146x^116+1992x^117+1428x^119+675x^120+792x^121+456x^123+66x^124+60x^128+51x^132+27x^136+12x^140+3x^144

The gray image is a linear code over GF(4) with n=152, k=7 and d=100.
This code was found by Heurico 1.16 in 0.762 seconds.