The generator matrix

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

generates a code of length 79 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+456x^225+732x^226+324x^227+30x^228+1284x^229+1320x^230+432x^231+66x^232+1344x^233+1416x^234+624x^235+51x^236+1260x^237+1116x^238+372x^239+48x^240+948x^241+912x^242+84x^243+21x^244+840x^245+828x^246+216x^247+18x^248+516x^249+420x^250+216x^251+15x^252+216x^253+144x^254+36x^255+3x^256+48x^257+24x^258+3x^276

The gray image is a linear code over GF(4) with n=316, k=7 and d=225.
This code was found by Heurico 1.16 in 1.67 seconds.