The generator matrix

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

generates a code of length 44 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+264x^121+468x^122+252x^123+75x^124+1308x^125+1332x^126+420x^127+45x^128+1632x^129+1728x^130+708x^131+30x^132+1440x^133+1584x^134+468x^135+42x^136+1392x^137+1260x^138+336x^139+30x^140+708x^141+540x^142+120x^143+18x^144+168x^145+6x^148+6x^152+3x^156

The gray image is a linear code over GF(4) with n=176, k=7 and d=121.
This code was found by Heurico 1.16 in 0.829 seconds.