The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 (a+1)X 1 0 1 1 1 (a+1)X aX 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 aX (a+1)X 0 (a+1)X 1 X 1 1 1 1 0 1 1 (a+1)X 1 1 1 aX aX 1 0 1 1 1 aX 1 1 1 1 1 1 1 1 0 1 0 0 0 (a+1)X 1 (a+1)X+a a+1 (a+1)X+1 1 (a+1)X+a a (a+1)X+a+1 1 (a+1)X+a+1 1 (a+1)X+1 a+1 a 1 1 (a+1)X+a+1 a+1 0 X+1 a 1 (a+1)X+a X+a+1 X X a+1 X+1 a a+1 aX 1 1 0 1 X 1 (a+1)X+1 aX+a (a+1)X+a+1 (a+1)X+1 1 (a+1)X+1 aX+1 1 (a+1)X X+a (a+1)X 1 0 aX 1 aX+a X aX+a 1 aX+a (a+1)X 1 aX+a+1 (a+1)X+a X+a (a+1)X 0 0 0 1 1 a a+1 1 X+1 1 0 a+1 X+a+1 a aX+a X+1 aX a a a+1 X X+a+1 0 X+1 (a+1)X+a (a+1)X+a X (a+1)X+a+1 (a+1)X+1 a aX+a+1 (a+1)X (a+1)X+a+1 aX X+a aX+1 aX+a aX+1 X+a X+a+1 1 (a+1)X+a+1 X+1 (a+1)X+a aX+a X+a+1 X aX+a+1 aX+1 aX+a+1 X+1 X aX aX aX aX+a 1 aX+1 X (a+1)X 0 aX aX+a+1 a (a+1)X+a (a+1)X+1 X+a+1 a aX+1 X (a+1)X 0 0 0 (a+1)X 0 0 0 aX aX aX (a+1)X X (a+1)X X (a+1)X X X aX (a+1)X X aX 0 (a+1)X X aX 0 aX 0 (a+1)X 0 X X 0 0 X 0 aX (a+1)X 0 (a+1)X 0 aX (a+1)X X X aX (a+1)X 0 (a+1)X (a+1)X aX aX 0 aX aX aX 0 (a+1)X X X (a+1)X 0 0 X 0 aX X 0 (a+1)X aX 0 0 0 0 X aX (a+1)X X 0 aX X (a+1)X aX 0 (a+1)X X X 0 aX 0 X (a+1)X (a+1)X aX X aX aX X X 0 aX (a+1)X 0 X X aX (a+1)X 0 0 X (a+1)X 0 X aX 0 0 aX aX (a+1)X 0 (a+1)X (a+1)X aX aX X aX 0 X X 0 aX aX aX (a+1)X 0 aX aX 0 X 0 generates a code of length 70 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 192. Homogenous weight enumerator: w(x)=1x^0+54x^192+144x^193+228x^194+720x^195+873x^196+984x^197+888x^198+1812x^199+1953x^200+1596x^201+1032x^202+2880x^203+2775x^204+2304x^205+1560x^206+3780x^207+3891x^208+3216x^209+1740x^210+4584x^211+4167x^212+3216x^213+1596x^214+4092x^215+3168x^216+2460x^217+1200x^218+2640x^219+1926x^220+1056x^221+720x^222+876x^223+450x^224+360x^225+216x^226+120x^227+96x^228+24x^229+36x^230+39x^232+36x^236+9x^240+12x^244+3x^252+3x^256 The gray image is a linear code over GF(4) with n=280, k=8 and d=192. This code was found by Heurico 1.16 in 20.4 seconds.