The generator matrix

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

generates a code of length 81 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+1617x^232+3279x^236+3519x^240+2625x^244+2169x^248+1473x^252+1140x^256+447x^260+114x^264

The gray image is a linear code over GF(4) with n=324, k=7 and d=232.
This code was found by Heurico 1.16 in 44 seconds.