The generator matrix

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

generates a code of length 37 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+66x^96+108x^97+168x^99+222x^100+396x^101+636x^103+390x^104+744x^105+1104x^107+999x^108+1608x^109+1944x^111+1326x^112+1836x^113+1704x^115+828x^116+1260x^117+588x^119+78x^120+192x^121+87x^124+54x^128+24x^132+18x^136+3x^144

The gray image is a linear code over GF(4) with n=148, k=7 and d=96.
This code was found by Heurico 1.16 in 0.738 seconds.