The generator matrix

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

generates a code of length 95 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+150x^268+72x^269+216x^271+537x^272+324x^273+372x^275+1539x^276+408x^277+492x^279+1635x^280+576x^281+444x^283+1911x^284+468x^285+516x^287+1707x^288+408x^289+456x^291+1434x^292+384x^293+372x^295+897x^296+288x^297+156x^299+237x^300+108x^301+36x^303+87x^304+36x^305+12x^307+6x^308+27x^312+30x^316+15x^320+15x^324+3x^328+3x^332+3x^336+3x^348

The gray image is a linear code over GF(4) with n=380, k=7 and d=268.
This code was found by Heurico 1.16 in 2.3 seconds.