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

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+492x^121+504x^122+552x^123+738x^124+2136x^125+1668x^126+1500x^127+1482x^128+3756x^129+3204x^130+2484x^131+2076x^132+5148x^133+4644x^134+2712x^135+2523x^136+6300x^137+4764x^138+3168x^139+2319x^140+4920x^141+3048x^142+1644x^143+942x^144+1644x^145+600x^146+228x^147+141x^148+180x^149+6x^152+3x^156+3x^160+3x^164+3x^168

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 13.9 seconds.