The generator matrix

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

generates a code of length 68 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+318x^192+420x^193+336x^194+636x^195+822x^196+1008x^197+444x^198+888x^199+1014x^200+1080x^201+408x^202+672x^203+984x^204+1140x^205+396x^206+684x^207+609x^208+864x^209+408x^210+552x^211+555x^212+516x^213+204x^214+300x^215+369x^216+276x^217+96x^218+108x^219+150x^220+72x^221+12x^222+24x^224+9x^228+9x^232

The gray image is a linear code over GF(4) with n=272, k=7 and d=192.
This code was found by Heurico 1.16 in 1.24 seconds.