The generator matrix

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

generates a code of length 70 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 195.

Homogenous weight enumerator: w(x)=1x^0+888x^195+855x^196+504x^197+1080x^198+2628x^199+1911x^200+912x^201+1452x^202+4332x^203+2748x^204+1308x^205+1776x^206+4860x^207+3300x^208+1464x^209+1824x^210+6012x^211+3516x^212+1584x^213+2328x^214+5268x^215+2883x^216+1068x^217+1404x^218+3552x^219+2055x^220+552x^221+768x^222+1296x^223+561x^224+252x^225+120x^226+336x^227+87x^228+36x^229+12x^231+3x^236

The gray image is a linear code over GF(4) with n=280, k=8 and d=195.
This code was found by Heurico 1.16 in 44.8 seconds.