The generator matrix

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

generates a code of length 45 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 124.

Homogenous weight enumerator: w(x)=1x^0+255x^124+456x^125+252x^126+324x^127+897x^128+1356x^129+552x^130+588x^131+1077x^132+1824x^133+564x^134+528x^135+1020x^136+1476x^137+396x^138+528x^139+987x^140+1188x^141+384x^142+300x^143+438x^144+576x^145+156x^146+36x^147+171x^148+36x^149+12x^152+6x^156

The gray image is a linear code over GF(4) with n=180, k=7 and d=124.
This code was found by Heurico 1.16 in 0.623 seconds.