The generator matrix

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

generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+330x^260+348x^261+516x^262+216x^263+477x^264+444x^265+336x^266+84x^267+258x^268+144x^269+108x^270+36x^271+114x^272+72x^273+48x^274+84x^276+60x^277+60x^278+36x^279+69x^280+12x^281+24x^282+24x^284+24x^285+36x^286+48x^288+48x^289+24x^290+12x^291+3x^304

The gray image is a linear code over GF(4) with n=356, k=6 and d=260.
This code was found by Heurico 1.16 in 9.69 seconds.