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

generates a code of length 48 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 137.

Homogenous weight enumerator: w(x)=1x^0+492x^137+96x^138+384x^139+264x^140+744x^141+120x^142+72x^143+189x^144+396x^145+96x^146+120x^147+108x^148+276x^149+24x^150+120x^151+42x^152+312x^153+48x^154+72x^155+36x^156+84x^157

The gray image is a linear code over GF(4) with n=192, k=6 and d=137.
This code was found by Heurico 1.16 in 6.83 seconds.