The generator matrix

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

generates a code of length 44 over F4[X]/(X^2) who´s minimum homogenous weight is 118.

Homogenous weight enumerator: w(x)=1x^0+204x^118+492x^119+681x^120+1104x^121+1320x^122+2064x^123+1749x^124+2136x^125+2520x^126+3564x^127+2484x^128+3048x^129+3324x^130+5412x^131+2940x^132+4212x^133+3780x^134+5976x^135+3291x^136+3156x^137+3048x^138+3420x^139+1764x^140+1476x^141+1080x^142+576x^143+375x^144+228x^145+84x^146+24x^148+3x^156

The gray image is a linear code over GF(4) with n=176, k=8 and d=118.
This code was found by Heurico 1.16 in 11.7 seconds.