The generator matrix

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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+768x^190+840x^191+162x^192+1836x^194+1212x^195+249x^196+1788x^198+1128x^199+174x^200+1776x^202+1188x^203+225x^204+1380x^206+900x^207+69x^208+984x^210+576x^211+93x^212+624x^214+252x^215+36x^216+60x^218+48x^219+6x^220+6x^224+3x^236

The gray image is a linear code over GF(4) with n=268, k=7 and d=190.
This code was found by Heurico 1.16 in 58.4 seconds.