The generator matrix

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

generates a code of length 91 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 260.

Homogenous weight enumerator: w(x)=1x^0+339x^260+252x^261+360x^262+564x^263+1191x^264+528x^265+612x^266+636x^267+1467x^268+696x^269+600x^270+432x^271+1257x^272+480x^273+516x^274+528x^275+951x^276+396x^277+348x^278+348x^279+840x^280+288x^281+312x^282+276x^283+549x^284+264x^285+204x^286+192x^287+462x^288+120x^289+48x^290+96x^291+78x^292+24x^293+72x^294+27x^296+24x^297+6x^304

The gray image is a linear code over GF(4) with n=364, k=7 and d=260.
This code was found by Heurico 1.16 in 1.51 seconds.