The generator matrix

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

generates a code of length 74 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 214.

Homogenous weight enumerator: w(x)=1x^0+276x^214+240x^215+267x^216+144x^217+660x^218+372x^219+132x^220+120x^221+420x^222+276x^223+42x^224+48x^225+252x^226+120x^227+66x^228+48x^229+120x^230+48x^231+96x^232+96x^234+36x^235+18x^236+24x^237+48x^238+60x^239+12x^240+48x^242+3x^248+3x^256

The gray image is a linear code over GF(4) with n=296, k=6 and d=214.
This code was found by Heurico 1.16 in 0.125 seconds.