The generator matrix

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

generates a code of length 89 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+258x^252+276x^253+168x^254+837x^256+708x^257+384x^258+1320x^260+948x^261+420x^262+984x^264+1236x^265+708x^266+1110x^268+984x^269+672x^270+1155x^272+972x^273+408x^274+846x^276+756x^277+276x^278+432x^280+252x^281+36x^282+114x^284+12x^285+21x^288+12x^292+18x^296+21x^300+24x^304+12x^308+3x^316

The gray image is a linear code over GF(4) with n=356, k=7 and d=252.
This code was found by Heurico 1.16 in 8.69 seconds.