The generator matrix

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

generates a code of length 44 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+210x^124+204x^125+48x^126+348x^127+549x^128+408x^129+72x^130+264x^131+324x^132+384x^133+156x^135+180x^136+240x^137+72x^138+144x^139+195x^140+84x^141+48x^143+135x^144+24x^145+3x^148+3x^152

The gray image is a linear code over GF(4) with n=176, k=6 and d=124.
This code was found by Heurico 1.16 in 0.047 seconds.