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

generates a code of length 93 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 264.

Homogenous weight enumerator: w(x)=1x^0+414x^264+180x^265+156x^267+1074x^268+372x^269+432x^271+1767x^272+540x^273+528x^275+1602x^276+420x^277+720x^279+1710x^280+504x^281+684x^283+1506x^284+540x^285+480x^287+1188x^288+348x^289+72x^291+753x^292+108x^293+111x^296+60x^297+12x^300+27x^304+21x^308+15x^312+6x^316+6x^320+9x^324+6x^328+6x^332+3x^336+3x^340

The gray image is a linear code over GF(4) with n=372, k=7 and d=264.
This code was found by Heurico 1.16 in 2.26 seconds.