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  0 aX  1  1  1  X  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  1  X (a+1)X+a+1 aX+1 (a+1)X+a  1 (a+1)X+1 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 (a+1)X+a+1 (a+1)X+a+1  1 (a+1)X+1  a  0  X (a+1)X+a+1 aX
 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  X aX (a+1)X (a+1)X (a+1)X  0  X aX  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+501x^116+612x^117+504x^118+348x^119+1422x^120+828x^121+744x^122+336x^123+1671x^124+1116x^125+636x^126+360x^127+1731x^128+1116x^129+684x^130+336x^131+1266x^132+720x^133+444x^134+156x^135+549x^136+216x^137+60x^138+15x^140+6x^144+3x^148+3x^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 16.7 seconds.