The generator matrix

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

generates a code of length 69 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 192.

Homogenous weight enumerator: w(x)=1x^0+246x^192+72x^193+192x^195+978x^196+348x^197+372x^199+1476x^200+420x^201+528x^203+1878x^204+684x^205+696x^207+1986x^208+624x^209+816x^211+1995x^212+564x^213+372x^215+1242x^216+324x^217+96x^219+285x^220+36x^221+51x^224+18x^228+36x^232+18x^236+12x^240+9x^244+6x^248+3x^252

The gray image is a linear code over GF(4) with n=276, k=7 and d=192.
This code was found by Heurico 1.16 in 1.58 seconds.