The generator matrix

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

generates a code of length 42 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 116.

Homogenous weight enumerator: w(x)=1x^0+450x^116+756x^117+468x^118+1401x^120+1344x^121+636x^122+1782x^124+1404x^125+900x^126+1725x^128+1284x^129+612x^130+1290x^132+960x^133+408x^134+495x^136+396x^137+48x^138+6x^140+12x^144+6x^152

The gray image is a linear code over GF(4) with n=168, k=7 and d=116.
This code was found by Heurico 1.16 in 1.2 seconds.