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

generates a code of length 40 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+39x^104+228x^107+147x^108+168x^109+144x^110+756x^111+168x^112+420x^113+384x^114+1476x^115+165x^116+624x^117+864x^118+2472x^119+114x^120+840x^121+1152x^122+2700x^123+87x^124+840x^125+528x^126+1476x^127+108x^128+180x^129+108x^131+75x^132+57x^136+33x^140+9x^144+18x^148+3x^156

The gray image is a linear code over GF(4) with n=160, k=7 and d=104.
This code was found by Heurico 1.16 in 0.8 seconds.