The generator matrix

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

generates a code of length 62 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+912x^175+420x^176+2412x^179+813x^180+2448x^183+972x^184+2592x^187+756x^188+1824x^191+603x^192+1308x^195+381x^196+672x^199+126x^200+120x^203+18x^204+3x^208+3x^224

The gray image is a linear code over GF(4) with n=248, k=7 and d=175.
This code was found by Heurico 1.16 in 1.37 seconds.