The generator matrix

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

generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+213x^248+204x^249+48x^250+576x^251+1296x^252+888x^253+264x^254+1920x^255+2394x^256+1524x^257+396x^258+2880x^259+3498x^260+2304x^261+420x^262+3444x^263+3786x^264+2724x^265+576x^266+3936x^267+5193x^268+2892x^269+516x^270+3456x^271+3915x^272+2220x^273+348x^274+2892x^275+3108x^276+1608x^277+348x^278+1668x^279+1515x^280+672x^281+72x^282+648x^283+450x^284+276x^285+84x^286+72x^287+141x^288+48x^289+12x^291+18x^292+33x^296+12x^300+15x^304+6x^308+3x^312+3x^316

The gray image is a linear code over GF(4) with n=356, k=8 and d=248.
This code was found by Heurico 1.16 in 29.2 seconds.