The generator matrix

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

generates a code of length 69 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+102x^184+324x^188+408x^192+144x^194+498x^196+816x^198+384x^200+2016x^202+411x^204+3744x^206+327x^208+3984x^210+348x^212+1584x^214+330x^216+270x^220+261x^224+138x^228+138x^232+99x^236+27x^240+24x^244+6x^248

The gray image is a linear code over GF(4) with n=276, k=7 and d=184.
This code was found by Heurico 1.16 in 3.17 seconds.