The generator matrix

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

generates a code of length 19 over F4[X]/(X^2) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+336x^48+276x^49+432x^50+96x^51+1377x^52+900x^53+624x^54+576x^55+2238x^56+1980x^57+1296x^58+864x^59+2610x^60+1452x^61+720x^62+579x^64+21x^68+6x^72

The gray image is a linear code over GF(4) with n=76, k=7 and d=48.
This code was found by Heurico 1.16 in 0.278 seconds.