The generator matrix

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

generates a code of length 67 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 184.

Homogenous weight enumerator: w(x)=1x^0+87x^184+72x^187+501x^188+216x^189+324x^191+1254x^192+336x^193+516x^195+1527x^196+504x^197+552x^199+2220x^200+768x^201+672x^203+2262x^204+744x^205+612x^207+1497x^208+432x^209+276x^211+687x^212+72x^213+48x^215+87x^216+30x^220+24x^224+21x^228+18x^232+9x^236+6x^240+3x^244+6x^248

The gray image is a linear code over GF(4) with n=268, k=7 and d=184.
This code was found by Heurico 1.16 in 1.52 seconds.