The generator matrix

 1  0  1  1  1  1  1  1  1  0  1  1  1  0  1  1  1  X  1  1  0  1 (a+1)X  1  1  1  X  1  1  1  X  1  1  1  1  1  1  1  1  1  1 (a+1)X  X  1  1  1
 0  1  1  a a+1  0 (a+1)X+1 (a+1)X+a+1  a  1  0 (a+1)X+1 (a+1)X+a+1  1  a  X (a+1)X+a+1  1 (a+1)X+1  a  1 (a+1)X+a+1  1  0 aX+a+1 aX+1  1  X X+a X+1  1 (a+1)X+a  0 X+1 X+1 (a+1)X+1 (a+1)X+a+1 (a+1)X+a (a+1)X aX+a+1 X+a  1  1  a (a+1)X+a  X
 0  0 (a+1)X  0  0  0  X aX  X  X  X (a+1)X (a+1)X aX aX aX  0  0 aX aX (a+1)X aX  0 (a+1)X  X  0 aX aX aX (a+1)X  X (a+1)X  X  X  X (a+1)X (a+1)X  X  X (a+1)X aX  0 aX aX  0  X
 0  0  0  X  0  X (a+1)X (a+1)X  X (a+1)X  0 (a+1)X  X  X  0  X (a+1)X  0 aX  X  X (a+1)X (a+1)X (a+1)X  X (a+1)X (a+1)X  X  0  0  0  0 aX  0 (a+1)X (a+1)X aX  X aX  X (a+1)X aX (a+1)X (a+1)X (a+1)X  X
 0  0  0  0 (a+1)X (a+1)X (a+1)X (a+1)X  0 aX  X aX  0 aX (a+1)X  X  X (a+1)X (a+1)X aX  X  0  X (a+1)X  X  0  X (a+1)X  X (a+1)X (a+1)X  0 aX (a+1)X  0  X  0 aX (a+1)X (a+1)X  X 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 124.

Homogenous weight enumerator: w(x)=1x^0+150x^124+72x^126+360x^127+741x^128+348x^130+744x^131+1014x^132+528x^134+1296x^135+1464x^136+984x^138+1872x^139+1974x^140+840x^142+1416x^143+1275x^144+300x^146+456x^147+393x^148+42x^152+48x^156+33x^160+15x^164+12x^168+6x^172

The gray image is a linear code over GF(4) with n=184, k=7 and d=124.
This code was found by Heurico 1.16 in 0.97 seconds.