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

generates a code of length 95 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 272.

Homogenous weight enumerator: w(x)=1x^0+504x^272+276x^273+228x^274+384x^275+1581x^276+432x^277+300x^278+792x^279+1497x^280+732x^281+204x^282+576x^283+1593x^284+528x^285+240x^286+504x^287+1098x^288+456x^289+300x^290+264x^291+1029x^292+240x^293+120x^294+288x^295+723x^296+240x^297+48x^298+156x^299+411x^300+84x^301+60x^302+84x^303+165x^304+72x^305+36x^306+12x^307+90x^308+12x^309+12x^311+12x^312

The gray image is a linear code over GF(4) with n=380, k=7 and d=272.
This code was found by Heurico 1.16 in 1.54 seconds.