The generator matrix

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

generates a code of length 31 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+636x^81+1248x^82+528x^83+69x^84+2808x^85+3108x^86+1428x^87+255x^88+5196x^89+6036x^90+2316x^91+279x^92+8724x^93+9516x^94+3108x^95+255x^96+7848x^97+6396x^98+1524x^99+117x^100+2436x^101+1344x^102+312x^103+30x^104+9x^108+6x^116+3x^120

The gray image is a linear code over GF(4) with n=124, k=8 and d=81.
This code was found by Heurico 1.16 in 538 seconds.