The generator matrix

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

generates a code of length 44 over F4[X]/(X^2) who´s minimum homogenous weight is 115.

Homogenous weight enumerator: w(x)=1x^0+636x^115+774x^116+1080x^117+4128x^119+2982x^120+3732x^121+9900x^123+6546x^124+8688x^125+20280x^127+12087x^128+15804x^129+31332x^131+17673x^132+21336x^133+32304x^135+15693x^136+16620x^137+19620x^139+8040x^140+5760x^141+4536x^143+1605x^144+708x^145+144x^147+66x^148+39x^152+18x^156+3x^160+3x^164+6x^168

The gray image is a linear code over GF(4) with n=176, k=9 and d=115.
This code was found by Heurico 1.16 in 766 seconds.