The generator matrix

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

generates a code of length 45 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+456x^121+288x^122+648x^123+1413x^124+1956x^125+1284x^126+1344x^127+2088x^128+3792x^129+1944x^130+2352x^131+3288x^132+5604x^133+3240x^134+2940x^135+4119x^136+6132x^137+2976x^138+3204x^139+3618x^140+4824x^141+2196x^142+1620x^143+1575x^144+1668x^145+360x^146+180x^147+264x^148+144x^149+9x^152+9x^156

The gray image is a linear code over GF(4) with n=180, k=8 and d=121.
This code was found by Heurico 1.16 in 13.7 seconds.