The generator matrix

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

generates a code of length 46 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+420x^123+363x^124+396x^125+168x^126+2292x^127+1056x^128+1296x^129+648x^130+4464x^131+1398x^132+1884x^133+1104x^134+8040x^135+2073x^136+2880x^137+1872x^138+9396x^139+2427x^140+3396x^141+1800x^142+8532x^143+1884x^144+1968x^145+552x^146+3384x^147+795x^148+468x^149+336x^151+153x^152+39x^156+21x^160+9x^164+12x^168+9x^172

The gray image is a linear code over GF(4) with n=184, k=8 and d=123.
This code was found by Heurico 1.16 in 46.6 seconds.