The generator matrix

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

generates a code of length 38 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+516x^104+444x^105+420x^106+348x^107+1188x^108+1104x^109+720x^110+336x^111+1872x^112+1068x^113+696x^114+360x^115+1824x^116+996x^117+912x^118+336x^119+1332x^120+840x^121+324x^122+156x^123+411x^124+156x^125+15x^128+6x^132+3x^140

The gray image is a linear code over GF(4) with n=152, k=7 and d=104.
This code was found by Heurico 1.16 in 0.641 seconds.