The generator matrix

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

generates a code of length 56 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+288x^153+444x^154+684x^155+1014x^156+1284x^157+1644x^158+1884x^159+2226x^160+2136x^161+3216x^162+2616x^163+2619x^164+2856x^165+4320x^166+2976x^167+3003x^168+3372x^169+4824x^170+3480x^171+2931x^172+3048x^173+3768x^174+2568x^175+2127x^176+1908x^177+1548x^178+948x^179+753x^180+444x^181+204x^182+204x^183+168x^184+24x^185+3x^188+3x^200

The gray image is a linear code over GF(4) with n=224, k=8 and d=153.
This code was found by Heurico 1.16 in 14.8 seconds.