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

generates a code of length 78 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 217.

Homogenous weight enumerator: w(x)=1x^0+36x^217+72x^218+84x^219+252x^220+204x^221+336x^222+228x^223+486x^224+384x^225+852x^226+588x^227+576x^228+432x^229+1056x^230+480x^231+816x^232+672x^233+1212x^234+516x^235+780x^236+456x^237+1440x^238+612x^239+627x^240+528x^241+924x^242+420x^243+324x^244+240x^245+240x^246+120x^247+96x^248+108x^249+12x^250+24x^251+33x^252+12x^253+33x^256+15x^260+12x^264+15x^268+9x^272+21x^276

The gray image is a linear code over GF(4) with n=312, k=7 and d=217.
This code was found by Heurico 1.16 in 6.4 seconds.