The generator matrix

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

generates a code of length 69 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 191.

Homogenous weight enumerator: w(x)=1x^0+300x^191+747x^192+336x^193+792x^194+1524x^195+1788x^196+1008x^197+1884x^198+2880x^199+3201x^200+1488x^201+2172x^202+3696x^203+3699x^204+1692x^205+2760x^206+4368x^207+3744x^208+1896x^209+2640x^210+4236x^211+3753x^212+1608x^213+1980x^214+2880x^215+2805x^216+816x^217+1212x^218+1272x^219+1137x^220+300x^221+384x^222+324x^223+102x^224+72x^225+24x^227+15x^228

The gray image is a linear code over GF(4) with n=276, k=8 and d=191.
This code was found by Heurico 1.16 in 18.3 seconds.