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

generates a code of length 41 over F4[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+219x^112+384x^113+336x^114+252x^115+1332x^116+708x^117+624x^118+336x^119+1659x^120+1296x^121+624x^122+408x^123+1620x^124+984x^125+1008x^126+288x^127+1593x^128+912x^129+384x^130+204x^131+624x^132+324x^133+96x^134+48x^135+111x^136+9x^144

The gray image is a linear code over GF(4) with n=164, k=7 and d=112.
This code was found by Heurico 1.16 in 0.547 seconds.