The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  X  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  X  X  X  X a*X a*X a*X a^2*X  X a*X a*X  X  X a^2*X  X a*X  0  X a^2*X  X a^2*X  0  0  X a^2*X  0
 0  0  X  0  0  0  0  X  X  X a*X a^2*X a^2*X a*X  X a*X  0 a*X  0  X a^2*X  0  X  X  X a*X  X  X  X a*X  X a^2*X  X a*X  X  X  0 a^2*X
 0  0  0  X  0  0  X a^2*X a^2*X a*X  0  0  X  X a*X a*X a^2*X a^2*X  0  X a^2*X a*X  X a^2*X a^2*X a*X a*X  0 a^2*X a^2*X a^2*X  0 a*X  0 a*X  0  X  0
 0  0  0  0  X  0 a^2*X  0 a^2*X  X a*X  X  0 a^2*X a^2*X a*X a^2*X  0 a^2*X a^2*X  X a*X a^2*X  0 a^2*X  0 a*X a^2*X a*X  X  X  X a^2*X  0  0  0  0 a^2*X
 0  0  0  0  0  X  X  X a^2*X a^2*X a^2*X a^2*X  0  0  X  X  0  X  X  X  X a*X a*X a^2*X  0  0  0 a^2*X a*X  X a*X  X a*X  X  X a*X a^2*X  X

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+261x^96+366x^100+444x^104+192x^105+498x^108+1728x^109+501x^112+5184x^113+450x^116+5184x^117+540x^120+426x^124+354x^128+168x^132+72x^136+12x^140+3x^144

The gray image is a linear code over GF(4) with n=152, k=7 and d=96.
This code was found by Heurico 1.16 in 77.1 seconds.