The generator matrix

 1  0  0  1  1  1  1  1  1  1 2a+2  1  1  1  1  1  1 2a+2  0  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1 2a+2  0  2  0  0  1  1  1  1
 0  1  0  1  a 3a+3 2a+2 2a+2  1 3a+2  1  a  0 a+1 2a+3 3a+2 2a+3  1  1 a+2  a 3a+1 2a a+3 2a+1 a+2 3a+2  3 2a+1  1 3a+3 2a 2a 2a  0  1  1  1 2a  2 2a+1  2 2a+1  0
 0  0  1 3a+3  a  1  1 3a+3  3 3a+3 3a+3  0 a+2  0  2  1  a  1  a 3a+1 2a a+1 3a+1 2a+3  1  a  3 3a+2 a+3  a  a 3a+2 2a a+2 a+3  1 3a+3 a+2  1  1  2 a+3 3a+3  2
 0  0  0  2  0  2  0  0 2a+2 2a 2a+2 2a+2 2a+2  2  2 2a+2  0 2a+2  2  2  0  0 2a  2  2 2a  0 2a 2a 2a+2 2a  2  0 2a  2 2a  0  0  2  2 2a+2  0 2a 2a
 0  0  0  0  2 2a+2 2a 2a+2  2  0  0 2a  2 2a  2 2a+2  0 2a  0 2a+2 2a  0 2a+2  2 2a 2a 2a+2  0 2a 2a 2a+2  2  2  0  0  0 2a 2a 2a+2  2  2  0  2 2a

generates a code of length 44 over GR(16,4) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+150x^116+36x^117+216x^118+636x^119+1200x^120+324x^121+1068x^122+1740x^123+3273x^124+696x^125+1716x^126+3108x^127+5229x^128+1368x^129+2748x^130+4248x^131+7875x^132+1764x^133+3168x^134+5028x^135+6768x^136+1572x^137+2724x^138+2940x^139+3537x^140+384x^141+564x^142+732x^143+510x^144+84x^146+66x^148+27x^152+24x^156+6x^160+3x^164+3x^168

The gray image is a code over GF(4) with n=176, k=8 and d=116.
This code was found by Heurico 1.16 in 12 seconds.