The generator matrix

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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+72x^109+564x^110+324x^111+429x^112+552x^113+1416x^114+600x^115+537x^116+708x^117+1896x^118+780x^119+678x^120+756x^121+1776x^122+804x^123+525x^124+708x^125+1476x^126+480x^127+306x^128+276x^129+552x^130+84x^131+63x^132+12x^136+3x^140+6x^144

The gray image is a linear code over GF(4) with n=160, k=7 and d=109.
This code was found by Heurico 1.16 in 0.547 seconds.