The generator matrix

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

generates a code of length 37 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 100.

Homogenous weight enumerator: w(x)=1x^0+228x^100+204x^101+120x^102+408x^103+1545x^104+480x^105+360x^106+696x^107+1974x^108+900x^109+432x^110+840x^111+2286x^112+732x^113+336x^114+744x^115+1782x^116+576x^117+216x^118+384x^119+861x^120+180x^121+72x^122+18x^124+3x^128+6x^132

The gray image is a linear code over GF(4) with n=148, k=7 and d=100.
This code was found by Heurico 1.16 in 0.472 seconds.