The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 1 X 1 1
0 X 0 0 0 0 X X X aX 0 X (a+1)X aX (a+1)X aX X 0 0 X 0 X aX X X aX aX aX (a+1)X X 0 (a+1)X 0 (a+1)X X (a+1)X (a+1)X (a+1)X X X X X 0 aX 0 0
0 0 X 0 0 X (a+1)X aX aX aX 0 0 aX aX 0 aX 0 aX (a+1)X X (a+1)X aX X (a+1)X 0 X X X 0 X 0 aX (a+1)X X X X X 0 X aX aX X 0 X aX X
0 0 0 X 0 (a+1)X 0 X aX (a+1)X X X X 0 X (a+1)X 0 X (a+1)X X (a+1)X (a+1)X aX 0 (a+1)X X aX (a+1)X (a+1)X (a+1)X X (a+1)X aX 0 aX aX X (a+1)X X (a+1)X X X (a+1)X (a+1)X (a+1)X X
0 0 0 0 X X X (a+1)X X X X aX 0 0 0 aX aX 0 (a+1)X aX aX X aX aX (a+1)X X 0 X aX 0 aX aX X aX aX 0 aX (a+1)X 0 aX (a+1)X X X (a+1)X (a+1)X aX
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+93x^124+189x^128+192x^130+162x^132+576x^134+150x^136+1344x^138+108x^140+960x^142+102x^144+60x^148+57x^152+27x^156+33x^160+30x^164+9x^168+3x^176
The gray image is a linear code over GF(4) with n=184, k=6 and d=124.
This code was found by Heurico 1.16 in 0.136 seconds.