The generator matrix

 1  0  0  0  1  1  1  X  1 aX  1  1  X  1  1  0  1  1 (a+1)X  1  1  1 (a+1)X  1  1  0  1  1  1  1  X  1  1  1  1  1  1  0  1  1  0 (a+1)X  1  1
 0  1  0  0  X  1 X+1  1 (a+1)X  1 (a+1)X+1  0  1 X+1 aX+1  1 aX+a  a  1 aX+1 (a+1)X+a+1 aX+a  1 X+a X+a+1  1 aX+1 X+a a+1  1  1 X+a+1  a aX+a+1 aX X+a+1 X+a  1 aX+a a+1  1  1 (a+1)X+1 (a+1)X+a
 0  0  1  0 (a+1)X+1  1 (a+1)X (a+1)X+1 aX+1  a aX (a+1)X+a aX+1 a+1  a a+1  0 aX+a a+1 aX+a+1 (a+1)X  1 X+1 a+1  0 (a+1)X aX+a (a+1)X+a aX+a+1 a+1 (a+1)X+a (a+1)X+a+1 X+1  1 (a+1)X+a X+1 X+a (a+1)X+1 aX+1 a+1 (a+1)X+a+1  X  1 (a+1)X+1
 0  0  0  1 a+1  X aX+a+1 aX+a+1  a aX (a+1)X+a aX (a+1)X+a (a+1)X  1 (a+1)X+1 X+1 aX+a+1 aX+a+1 aX+a (a+1)X (a+1)X+1 (a+1)X+1 a+1 (a+1)X+a+1 a+1 (a+1)X+a (a+1)X+a (a+1)X+1 X+a+1 X+a+1 X+a+1  0  a aX+a+1  X  0  X aX+a+1 aX+a aX+a (a+1)X+a (a+1)X+a+1 aX+a

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

Homogenous weight enumerator: w(x)=1x^0+264x^118+468x^119+828x^120+672x^121+1560x^122+2136x^123+1953x^124+1524x^125+2736x^126+3456x^127+3099x^128+2352x^129+4260x^130+4620x^131+4044x^132+2604x^133+4764x^134+5088x^135+3834x^136+2580x^137+3492x^138+3564x^139+2223x^140+912x^141+1308x^142+636x^143+384x^144+108x^145+48x^146+6x^148+6x^152+6x^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 10.7 seconds.